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<?php
/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2013 PHPExcel
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * @category    PHPExcel
 * @package             PHPExcel_Calculation
 * @copyright   Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license             http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt   LGPL
 * @version             ##VERSION##, ##DATE##
 */


/** PHPExcel root directory */
if (!defined('PHPEXCEL_ROOT')) {
        /**
         * @ignore
         */
        define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
        require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
}


require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/trendClass.php';


/** LOG_GAMMA_X_MAX_VALUE */
define('LOG_GAMMA_X_MAX_VALUE', 2.55e305);

/** XMININ */
define('XMININ', 2.23e-308);

/** EPS */
define('EPS', 2.22e-16);

/** SQRT2PI */
define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099);


/**
 * PHPExcel_Calculation_Statistical
 *
 * @category    PHPExcel
 * @package             PHPExcel_Calculation
 * @copyright   Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Calculation_Statistical {


        private static function _checkTrendArrays(&$array1,&$array2) {
                if (!is_array($array1)) { $array1 = array($array1); }
                if (!is_array($array2)) { $array2 = array($array2); }

                $array1 = PHPExcel_Calculation_Functions::flattenArray($array1);
                $array2 = PHPExcel_Calculation_Functions::flattenArray($array2);
                foreach($array1 as $key => $value) {
                        if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
                                unset($array1[$key]);
                                unset($array2[$key]);
                        }
                }
                foreach($array2 as $key => $value) {
                        if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
                                unset($array1[$key]);
                                unset($array2[$key]);
                        }
                }
                $array1 = array_merge($array1);
                $array2 = array_merge($array2);

                return True;
        }       //      function _checkTrendArrays()


        /**
         * Beta function.
         *
         * @author Jaco van Kooten
         *
         * @param p require p>0
         * @param q require q>0
         * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
         */
        private static function _beta($p, $q) {
                if ($p <= 0.0 || $q <= 0.0 || ($p + $q) > LOG_GAMMA_X_MAX_VALUE) {
                        return 0.0;
                } else {
                        return exp(self::_logBeta($p, $q));
                }
        }       //      function _beta()


        /**
         * Incomplete beta function
         *
         * @author Jaco van Kooten
         * @author Paul Meagher
         *
         * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
         * @param x require 0<=x<=1
         * @param p require p>0
         * @param q require q>0
         * @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
         */
        private static function _incompleteBeta($x, $p, $q) {
                if ($x <= 0.0) {
                        return 0.0;
                } elseif ($x >= 1.0) {
                        return 1.0;
                } elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
                        return 0.0;
                }
                $beta_gam = exp((0 - self::_logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
                if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
                        return $beta_gam * self::_betaFraction($x, $p, $q) / $p;
                } else {
                        return 1.0 - ($beta_gam * self::_betaFraction(1 - $x, $q, $p) / $q);
                }
        }       //      function _incompleteBeta()


        // Function cache for _logBeta function
        private static $_logBetaCache_p                 = 0.0;
        private static $_logBetaCache_q                 = 0.0;
        private static $_logBetaCache_result    = 0.0;

        /**
         * The natural logarithm of the beta function.
         *
         * @param p require p>0
         * @param q require q>0
         * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
         * @author Jaco van Kooten
         */
        private static function _logBeta($p, $q) {
                if ($p != self::$_logBetaCache_p || $q != self::$_logBetaCache_q) {
                        self::$_logBetaCache_p = $p;
                        self::$_logBetaCache_q = $q;
                        if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
                                self::$_logBetaCache_result = 0.0;
                        } else {
                                self::$_logBetaCache_result = self::_logGamma($p) + self::_logGamma($q) - self::_logGamma($p + $q);
                        }
                }
                return self::$_logBetaCache_result;
        }       //      function _logBeta()


        /**
         * Evaluates of continued fraction part of incomplete beta function.
         * Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
         * @author Jaco van Kooten
         */
        private static function _betaFraction($x, $p, $q) {
                $c = 1.0;
                $sum_pq = $p + $q;
                $p_plus = $p + 1.0;
                $p_minus = $p - 1.0;
                $h = 1.0 - $sum_pq * $x / $p_plus;
                if (abs($h) < XMININ) {
                        $h = XMININ;
                }
                $h = 1.0 / $h;
                $frac = $h;
                $m       = 1;
                $delta = 0.0;
                while ($m <= MAX_ITERATIONS && abs($delta-1.0) > PRECISION ) {
                        $m2 = 2 * $m;
                        // even index for d
                        $d = $m * ($q - $m) * $x / ( ($p_minus + $m2) * ($p + $m2));
                        $h = 1.0 + $d * $h;
                        if (abs($h) < XMININ) {
                                $h = XMININ;
                        }
                        $h = 1.0 / $h;
                        $c = 1.0 + $d / $c;
                        if (abs($c) < XMININ) {
                                $c = XMININ;
                        }
                        $frac *= $h * $c;
                        // odd index for d
                        $d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
                        $h = 1.0 + $d * $h;
                        if (abs($h) < XMININ) {
                                $h = XMININ;
                        }
                        $h = 1.0 / $h;
                        $c = 1.0 + $d / $c;
                        if (abs($c) < XMININ) {
                                $c = XMININ;
                        }
                        $delta = $h * $c;
                        $frac *= $delta;
                        ++$m;
                }
                return $frac;
        }       //      function _betaFraction()


        /**
         * logGamma function
         *
         * @version 1.1
         * @author Jaco van Kooten
         *
         * Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
         *
         * The natural logarithm of the gamma function. <br />
         * Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
         * Applied Mathematics Division <br />
         * Argonne National Laboratory <br />
         * Argonne, IL 60439 <br />
         * <p>
         * References:
         * <ol>
         * <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
         *       Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
         * <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
         * <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
         * </ol>
         * </p>
         * <p>
         * From the original documentation:
         * </p>
         * <p>
         * This routine calculates the LOG(GAMMA) function for a positive real argument X.
         * Computation is based on an algorithm outlined in references 1 and 2.
         * The program uses rational functions that theoretically approximate LOG(GAMMA)
         * to at least 18 significant decimal digits. The approximation for X > 12 is from
         * reference 3, while approximations for X < 12.0 are similar to those in reference
         * 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
         * the compiler, the intrinsic functions, and proper selection of the
         * machine-dependent constants.
         * </p>
         * <p>
         * Error returns: <br />
         * The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
         * The computation is believed to be free of underflow and overflow.
         * </p>
         * @return MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
         */

        // Function cache for logGamma
        private static $_logGammaCache_result   = 0.0;
        private static $_logGammaCache_x                = 0.0;

        private static function _logGamma($x) {
                // Log Gamma related constants
                static $lg_d1 = -0.5772156649015328605195174;
                static $lg_d2 = 0.4227843350984671393993777;
                static $lg_d4 = 1.791759469228055000094023;

                static $lg_p1 = array(  4.945235359296727046734888,
                                                                201.8112620856775083915565,
                                                                2290.838373831346393026739,
                                                                11319.67205903380828685045,
                                                                28557.24635671635335736389,
                                                                38484.96228443793359990269,
                                                                26377.48787624195437963534,
                                                                7225.813979700288197698961 );
                static $lg_p2 = array(  4.974607845568932035012064,
                                                                542.4138599891070494101986,
                                                                15506.93864978364947665077,
                                                                184793.2904445632425417223,
                                                                1088204.76946882876749847,
                                                                3338152.967987029735917223,
                                                                5106661.678927352456275255,
                                                                3074109.054850539556250927 );
                static $lg_p4 = array(  14745.02166059939948905062,
                                                                2426813.369486704502836312,
                                                                121475557.4045093227939592,
                                                                2663432449.630976949898078,
                                                                29403789566.34553899906876,
                                                                170266573776.5398868392998,
                                                                492612579337.743088758812,
                                                                560625185622.3951465078242 );

                static $lg_q1 = array(  67.48212550303777196073036,
                                                                1113.332393857199323513008,
                                                                7738.757056935398733233834,
                                                                27639.87074403340708898585,
                                                                54993.10206226157329794414,
                                                                61611.22180066002127833352,
                                                                36351.27591501940507276287,
                                                                8785.536302431013170870835 );
                static $lg_q2 = array(  183.0328399370592604055942,
                                                                7765.049321445005871323047,
                                                                133190.3827966074194402448,
                                                                1136705.821321969608938755,
                                                                5267964.117437946917577538,
                                                                13467014.54311101692290052,
                                                                17827365.30353274213975932,
                                                                9533095.591844353613395747 );
                static $lg_q4 = array(  2690.530175870899333379843,
                                                                639388.5654300092398984238,
                                                                41355999.30241388052042842,
                                                                1120872109.61614794137657,
                                                                14886137286.78813811542398,
                                                                101680358627.2438228077304,
                                                                341747634550.7377132798597,
                                                                446315818741.9713286462081 );

                static $lg_c  = array(  -0.001910444077728,
                                                                8.4171387781295e-4,
                                                                -5.952379913043012e-4,
                                                                7.93650793500350248e-4,
                                                                -0.002777777777777681622553,
                                                                0.08333333333333333331554247,
                                                                0.0057083835261 );

        // Rough estimate of the fourth root of logGamma_xBig
        static $lg_frtbig = 2.25e76;
        static $pnt68    = 0.6796875;


        if ($x == self::$_logGammaCache_x) {
                return self::$_logGammaCache_result;
        }
        $y = $x;
        if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) {
                if ($y <= EPS) {
                        $res = -log(y);
                } elseif ($y <= 1.5) {
                        // ---------------------
                        //      EPS .LT. X .LE. 1.5
                        // ---------------------
                        if ($y < $pnt68) {
                                $corr = -log($y);
                                $xm1 = $y;
                        } else {
                                $corr = 0.0;
                                $xm1 = $y - 1.0;
                        }
                        if ($y <= 0.5 || $y >= $pnt68) {
                                $xden = 1.0;
                                $xnum = 0.0;
                                for ($i = 0; $i < 8; ++$i) {
                                        $xnum = $xnum * $xm1 + $lg_p1[$i];
                                        $xden = $xden * $xm1 + $lg_q1[$i];
                                }
                                $res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
                        } else {
                                $xm2 = $y - 1.0;
                                $xden = 1.0;
                                $xnum = 0.0;
                                for ($i = 0; $i < 8; ++$i) {
                                        $xnum = $xnum * $xm2 + $lg_p2[$i];
                                        $xden = $xden * $xm2 + $lg_q2[$i];
                                }
                                $res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
                        }
                } elseif ($y <= 4.0) {
                        // ---------------------
                        //      1.5 .LT. X .LE. 4.0
                        // ---------------------
                        $xm2 = $y - 2.0;
                        $xden = 1.0;
                        $xnum = 0.0;
                        for ($i = 0; $i < 8; ++$i) {
                                $xnum = $xnum * $xm2 + $lg_p2[$i];
                                $xden = $xden * $xm2 + $lg_q2[$i];
                        }
                        $res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
                } elseif ($y <= 12.0) {
                        // ----------------------
                        //      4.0 .LT. X .LE. 12.0
                        // ----------------------
                        $xm4 = $y - 4.0;
                        $xden = -1.0;
                        $xnum = 0.0;
                        for ($i = 0; $i < 8; ++$i) {
                                $xnum = $xnum * $xm4 + $lg_p4[$i];
                                $xden = $xden * $xm4 + $lg_q4[$i];
                        }
                        $res = $lg_d4 + $xm4 * ($xnum / $xden);
                } else {
                        // ---------------------------------
                        //      Evaluate for argument .GE. 12.0
                        // ---------------------------------
                        $res = 0.0;
                        if ($y <= $lg_frtbig) {
                                $res = $lg_c[6];
                                $ysq = $y * $y;
                                for ($i = 0; $i < 6; ++$i)
                                        $res = $res / $ysq + $lg_c[$i];
                                }
                                $res /= $y;
                                $corr = log($y);
                                $res = $res + log(SQRT2PI) - 0.5 * $corr;
                                $res += $y * ($corr - 1.0);
                        }
                } else {
                        // --------------------------
                        //      Return for bad arguments
                        // --------------------------
                        $res = MAX_VALUE;
                }
                // ------------------------------
                //      Final adjustments and return
                // ------------------------------
                self::$_logGammaCache_x = $x;
                self::$_logGammaCache_result = $res;
                return $res;
        }       //      function _logGamma()


        //
        //      Private implementation of the incomplete Gamma function
        //
        private static function _incompleteGamma($a,$x) {
                static $max = 32;
                $summer = 0;
                for ($n=0; $n<=$max; ++$n) {
                        $divisor = $a;
                        for ($i=1; $i<=$n; ++$i) {
                                $divisor *= ($a + $i);
                        }
                        $summer += (pow($x,$n) / $divisor);
                }
                return pow($x,$a) * exp(0-$x) * $summer;
        }       //      function _incompleteGamma()


        //
        //      Private implementation of the Gamma function
        //
        private static function _gamma($data) {
                if ($data == 0.0) return 0;

                static $p0 = 1.000000000190015;
                static $p = array ( 1 => 76.18009172947146,
                                                        2 => -86.50532032941677,
                                                        3 => 24.01409824083091,
                                                        4 => -1.231739572450155,
                                                        5 => 1.208650973866179e-3,
                                                        6 => -5.395239384953e-6
                                                  );

                $y = $x = $data;
                $tmp = $x + 5.5;
                $tmp -= ($x + 0.5) * log($tmp);

                $summer = $p0;
                for ($j=1;$j<=6;++$j) {
                        $summer += ($p[$j] / ++$y);
                }
                return exp(0 - $tmp + log(SQRT2PI * $summer / $x));
        }       //      function _gamma()


        /***************************************************************************
         *                                                              inverse_ncdf.php
         *                                                      -------------------
         *      begin                           : Friday, January 16, 2004
         *      copyright                       : (C) 2004 Michael Nickerson
         *      email                           : nickersonm@yahoo.com
         *
         ***************************************************************************/
        private static function _inverse_ncdf($p) {
                //      Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
                //      PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
                //      a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
                //      I have not checked the accuracy of this implementation. Be aware that PHP
                //      will truncate the coeficcients to 14 digits.

                //      You have permission to use and distribute this function freely for
                //      whatever purpose you want, but please show common courtesy and give credit
                //      where credit is due.

                //      Input paramater is $p - probability - where 0 < p < 1.

                //      Coefficients in rational approximations
                static $a = array(      1 => -3.969683028665376e+01,
                                                        2 => 2.209460984245205e+02,
                                                        3 => -2.759285104469687e+02,
                                                        4 => 1.383577518672690e+02,
                                                        5 => -3.066479806614716e+01,
                                                        6 => 2.506628277459239e+00
                                                 );

                static $b = array(      1 => -5.447609879822406e+01,
                                                        2 => 1.615858368580409e+02,
                                                        3 => -1.556989798598866e+02,
                                                        4 => 6.680131188771972e+01,
                                                        5 => -1.328068155288572e+01
                                                 );

                static $c = array(      1 => -7.784894002430293e-03,
                                                        2 => -3.223964580411365e-01,
                                                        3 => -2.400758277161838e+00,
                                                        4 => -2.549732539343734e+00,
                                                        5 => 4.374664141464968e+00,
                                                        6 => 2.938163982698783e+00
                                                 );

                static $d = array(      1 => 7.784695709041462e-03,
                                                        2 => 3.224671290700398e-01,
                                                        3 => 2.445134137142996e+00,
                                                        4 => 3.754408661907416e+00
                                                 );

                //      Define lower and upper region break-points.
                $p_low = 0.02425;                       //Use lower region approx. below this
                $p_high = 1 - $p_low;           //Use upper region approx. above this

                if (0 < $p && $p < $p_low) {
                        //      Rational approximation for lower region.
                        $q = sqrt(-2 * log($p));
                        return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
                                        (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
                } elseif ($p_low <= $p && $p <= $p_high) {
                        //      Rational approximation for central region.
                        $q = $p - 0.5;
                        $r = $q * $q;
                        return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
                                   ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
                } elseif ($p_high < $p && $p < 1) {
                        //      Rational approximation for upper region.
                        $q = sqrt(-2 * log(1 - $p));
                        return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
                                         (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
                }
                //      If 0 < p < 1, return a null value
                return PHPExcel_Calculation_Functions::NULL();
        }       //      function _inverse_ncdf()


        private static function _inverse_ncdf2($prob) {
                //      Approximation of inverse standard normal CDF developed by
                //      B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58.

                $a1 = 2.50662823884;
                $a2 = -18.61500062529;
                $a3 = 41.39119773534;
                $a4 = -25.44106049637;

                $b1 = -8.4735109309;
                $b2 = 23.08336743743;
                $b3 = -21.06224101826;
                $b4 = 3.13082909833;

                $c1 = 0.337475482272615;
                $c2 = 0.976169019091719;
                $c3 = 0.160797971491821;
                $c4 = 2.76438810333863E-02;
                $c5 = 3.8405729373609E-03;
                $c6 = 3.951896511919E-04;
                $c7 = 3.21767881768E-05;
                $c8 = 2.888167364E-07;
                $c9 = 3.960315187E-07;

                $y = $prob - 0.5;
                if (abs($y) < 0.42) {
                        $z = ($y * $y);
                        $z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1);
                } else {
                        if ($y > 0) {
                                $z = log(-log(1 - $prob));
                        } else {
                                $z = log(-log($prob));
                        }
                        $z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9)))))));
                        if ($y < 0) {
                                $z = -$z;
                        }
                }
                return $z;
        }       //      function _inverse_ncdf2()


        private static function _inverse_ncdf3($p) {
                //      ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3.
                //      Produces the normal deviate Z corresponding to a given lower
                //      tail area of P; Z is accurate to about 1 part in 10**16.
                //
                //      This is a PHP version of the original FORTRAN code that can
                //      be found at http://lib.stat.cmu.edu/apstat/
                $split1 = 0.425;
                $split2 = 5;
                $const1 = 0.180625;
                $const2 = 1.6;

                //      coefficients for p close to 0.5
                $a0 = 3.3871328727963666080;
                $a1 = 1.3314166789178437745E+2;
                $a2 = 1.9715909503065514427E+3;
                $a3 = 1.3731693765509461125E+4;
                $a4 = 4.5921953931549871457E+4;
                $a5 = 6.7265770927008700853E+4;
                $a6 = 3.3430575583588128105E+4;
                $a7 = 2.5090809287301226727E+3;

                $b1 = 4.2313330701600911252E+1;
                $b2 = 6.8718700749205790830E+2;
                $b3 = 5.3941960214247511077E+3;
                $b4 = 2.1213794301586595867E+4;
                $b5 = 3.9307895800092710610E+4;
                $b6 = 2.8729085735721942674E+4;
                $b7 = 5.2264952788528545610E+3;

                //      coefficients for p not close to 0, 0.5 or 1.
                $c0 = 1.42343711074968357734;
                $c1 = 4.63033784615654529590;
                $c2 = 5.76949722146069140550;
                $c3 = 3.64784832476320460504;
                $c4 = 1.27045825245236838258;
                $c5 = 2.41780725177450611770E-1;
                $c6 = 2.27238449892691845833E-2;
                $c7 = 7.74545014278341407640E-4;

                $d1 = 2.05319162663775882187;
                $d2 = 1.67638483018380384940;
                $d3 = 6.89767334985100004550E-1;
                $d4 = 1.48103976427480074590E-1;
                $d5 = 1.51986665636164571966E-2;
                $d6 = 5.47593808499534494600E-4;
                $d7 = 1.05075007164441684324E-9;

                //      coefficients for p near 0 or 1.
                $e0 = 6.65790464350110377720;
                $e1 = 5.46378491116411436990;
                $e2 = 1.78482653991729133580;
                $e3 = 2.96560571828504891230E-1;
                $e4 = 2.65321895265761230930E-2;
                $e5 = 1.24266094738807843860E-3;
                $e6 = 2.71155556874348757815E-5;
                $e7 = 2.01033439929228813265E-7;

                $f1 = 5.99832206555887937690E-1;
                $f2 = 1.36929880922735805310E-1;
                $f3 = 1.48753612908506148525E-2;
                $f4 = 7.86869131145613259100E-4;
                $f5 = 1.84631831751005468180E-5;
                $f6 = 1.42151175831644588870E-7;
                $f7 = 2.04426310338993978564E-15;

                $q = $p - 0.5;

                //      computation for p close to 0.5
                if (abs($q) <= split1) {
                        $R = $const1 - $q * $q;
                        $z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) /
                                          ((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1);
                } else {
                        if ($q < 0) {
                                $R = $p;
                        } else {
                                $R = 1 - $p;
                        }
                        $R = pow(-log($R),2);

                        //      computation for p not close to 0, 0.5 or 1.
                        If ($R <= $split2) {
                                $R = $R - $const2;
                                $z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) /
                                         ((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1);
                        } else {
                        //      computation for p near 0 or 1.
                                $R = $R - $split2;
                                $z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) /
                                         ((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1);
                        }
                        if ($q < 0) {
                                $z = -$z;
                        }
                }
                return $z;
        }       //      function _inverse_ncdf3()


        /**
         * AVEDEV
         *
         * Returns the average of the absolute deviations of data points from their mean.
         * AVEDEV is a measure of the variability in a data set.
         *
         * Excel Function:
         *              AVEDEV(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function AVEDEV() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

                // Return value
                $returnValue = null;

                $aMean = self::AVERAGE($aArgs);
                if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
                        $aCount = 0;
                        foreach ($aArgs as $k => $arg) {
                                if ((is_bool($arg)) &&
                                        ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
                                        $arg = (integer) $arg;
                                }
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        if (is_null($returnValue)) {
                                                $returnValue = abs($arg - $aMean);
                                        } else {
                                                $returnValue += abs($arg - $aMean);
                                        }
                                        ++$aCount;
                                }
                        }

                        // Return
                        if ($aCount == 0) {
                                return PHPExcel_Calculation_Functions::DIV0();
                        }
                        return $returnValue / $aCount;
                }
                return PHPExcel_Calculation_Functions::NaN();
        }       //      function AVEDEV()


        /**
         * AVERAGE
         *
         * Returns the average (arithmetic mean) of the arguments
         *
         * Excel Function:
         *              AVERAGE(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function AVERAGE() {
                $returnValue = $aCount = 0;

                // Loop through arguments
                foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
                        if ((is_bool($arg)) &&
                                ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
                                $arg = (integer) $arg;
                        }
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                if (is_null($returnValue)) {
                                        $returnValue = $arg;
                                } else {
                                        $returnValue += $arg;
                                }
                                ++$aCount;
                        }
                }

                // Return
                if ($aCount > 0) {
                        return $returnValue / $aCount;
                } else {
                        return PHPExcel_Calculation_Functions::DIV0();
                }
        }       //      function AVERAGE()


        /**
         * AVERAGEA
         *
         * Returns the average of its arguments, including numbers, text, and logical values
         *
         * Excel Function:
         *              AVERAGEA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function AVERAGEA() {
                // Return value
                $returnValue = null;

                $aCount = 0;
                // Loop through arguments
                foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
                        if ((is_bool($arg)) &&
                                (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                        } else {
                                if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
                                        if (is_bool($arg)) {
                                                $arg = (integer) $arg;
                                        } elseif (is_string($arg)) {
                                                $arg = 0;
                                        }
                                        if (is_null($returnValue)) {
                                                $returnValue = $arg;
                                        } else {
                                                $returnValue += $arg;
                                        }
                                        ++$aCount;
                                }
                        }
                }

                // Return
                if ($aCount > 0) {
                        return $returnValue / $aCount;
                } else {
                        return PHPExcel_Calculation_Functions::DIV0();
                }
        }       //      function AVERAGEA()


        /**
         * AVERAGEIF
         *
         * Returns the average value from a range of cells that contain numbers within the list of arguments
         *
         * Excel Function:
         *              AVERAGEIF(value1[,value2[, ...]],condition)
         *
         * @access      public
         * @category Mathematical and Trigonometric Functions
         * @param       mixed           $arg,...                Data values
         * @param       string          $condition              The criteria that defines which cells will be checked.
         * @param       mixed[]         $averageArgs    Data values
         * @return      float
         */
        public static function AVERAGEIF($aArgs,$condition,$averageArgs = array()) {
                // Return value
                $returnValue = 0;

                $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
                $averageArgs = PHPExcel_Calculation_Functions::flattenArray($averageArgs);
                if (empty($averageArgs)) {
                        $averageArgs = $aArgs;
                }
                $condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
                // Loop through arguments
                $aCount = 0;
                foreach ($aArgs as $key => $arg) {
                        if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
                        $testCondition = '='.$arg.$condition;
                        if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
                                if ((is_null($returnValue)) || ($arg > $returnValue)) {
                                        $returnValue += $arg;
                                        ++$aCount;
                                }
                        }
                }

                // Return
                if ($aCount > 0) {
                        return $returnValue / $aCount;
                } else {
                        return PHPExcel_Calculation_Functions::DIV0();
                }
        }       //      function AVERAGEIF()


        /**
         * BETADIST
         *
         * Returns the beta distribution.
         *
         * @param       float           $value                  Value at which you want to evaluate the distribution
         * @param       float           $alpha                  Parameter to the distribution
         * @param       float           $beta                   Parameter to the distribution
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function BETADIST($value,$alpha,$beta,$rMin=0,$rMax=1) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $alpha  = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
                $beta   = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
                $rMin   = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
                $rMax   = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);

                if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
                        if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ($rMin > $rMax) {
                                $tmp = $rMin;
                                $rMin = $rMax;
                                $rMax = $tmp;
                        }
                        $value -= $rMin;
                        $value /= ($rMax - $rMin);
                        return self::_incompleteBeta($value,$alpha,$beta);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BETADIST()


        /**
         * BETAINV
         *
         * Returns the inverse of the beta distribution.
         *
         * @param       float           $probability    Probability at which you want to evaluate the distribution
         * @param       float           $alpha                  Parameter to the distribution
         * @param       float           $beta                   Parameter to the distribution
         * @param       float           $rMin                   Minimum value
         * @param       float           $rMax                   Maximum value
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function BETAINV($probability,$alpha,$beta,$rMin=0,$rMax=1) {
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $alpha                  = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
                $beta                   = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
                $rMin                   = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
                $rMax                   = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);

                if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
                        if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ($rMin > $rMax) {
                                $tmp = $rMin;
                                $rMin = $rMax;
                                $rMax = $tmp;
                        }
                        $a = 0;
                        $b = 2;

                        $i = 0;
                        while ((($b - $a) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
                                $guess = ($a + $b) / 2;
                                $result = self::BETADIST($guess, $alpha, $beta);
                                if (($result == $probability) || ($result == 0)) {
                                        $b = $a;
                                } elseif ($result > $probability) {
                                        $b = $guess;
                                } else {
                                        $a = $guess;
                                }
                        }
                        if ($i == MAX_ITERATIONS) {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                        return round($rMin + $guess * ($rMax - $rMin),12);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BETAINV()


        /**
         * BINOMDIST
         *
         * Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
         *              a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
         *              when trials are independent, and when the probability of success is constant throughout the
         *              experiment. For example, BINOMDIST can calculate the probability that two of the next three
         *              babies born are male.
         *
         * @param       float           $value                  Number of successes in trials
         * @param       float           $trials                 Number of trials
         * @param       float           $probability    Probability of success on each trial
         * @param       boolean         $cumulative
         * @return      float
         *
         * @todo        Cumulative distribution function
         *
         */
        public static function BINOMDIST($value, $trials, $probability, $cumulative) {
                $value                  = floor(PHPExcel_Calculation_Functions::flattenSingleValue($value));
                $trials                 = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);

                if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
                        if (($value < 0) || ($value > $trials)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($probability < 0) || ($probability > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
                                if ($cumulative) {
                                        $summer = 0;
                                        for ($i = 0; $i <= $value; ++$i) {
                                                $summer += PHPExcel_Calculation_MathTrig::COMBIN($trials,$i) * pow($probability,$i) * pow(1 - $probability,$trials - $i);
                                        }
                                        return $summer;
                                } else {
                                        return PHPExcel_Calculation_MathTrig::COMBIN($trials,$value) * pow($probability,$value) * pow(1 - $probability,$trials - $value) ;
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BINOMDIST()


        /**
         * CHIDIST
         *
         * Returns the one-tailed probability of the chi-squared distribution.
         *
         * @param       float           $value                  Value for the function
         * @param       float           $degrees                degrees of freedom
         * @return      float
         */
        public static function CHIDIST($value, $degrees) {
                $value          = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $degrees        = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));

                if ((is_numeric($value)) && (is_numeric($degrees))) {
                        if ($degrees < 1) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ($value < 0) {
                                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                                        return 1;
                                }
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return 1 - (self::_incompleteGamma($degrees/2,$value/2) / self::_gamma($degrees/2));
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function CHIDIST()


        /**
         * CHIINV
         *
         * Returns the one-tailed probability of the chi-squared distribution.
         *
         * @param       float           $probability    Probability for the function
         * @param       float           $degrees                degrees of freedom
         * @return      float
         */
        public static function CHIINV($probability, $degrees) {
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $degrees                = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));

                if ((is_numeric($probability)) && (is_numeric($degrees))) {

                        $xLo = 100;
                        $xHi = 0;

                        $x = $xNew = 1;
                        $dx     = 1;
                        $i = 0;

                        while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
                                // Apply Newton-Raphson step
                                $result = self::CHIDIST($x, $degrees);
                                $error = $result - $probability;
                                if ($error == 0.0) {
                                        $dx = 0;
                                } elseif ($error < 0.0) {
                                        $xLo = $x;
                                } else {
                                        $xHi = $x;
                                }
                                // Avoid division by zero
                                if ($result != 0.0) {
                                        $dx = $error / $result;
                                        $xNew = $x - $dx;
                                }
                                // If the NR fails to converge (which for example may be the
                                // case if the initial guess is too rough) we apply a bisection
                                // step to determine a more narrow interval around the root.
                                if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
                                        $xNew = ($xLo + $xHi) / 2;
                                        $dx = $xNew - $x;
                                }
                                $x = $xNew;
                        }
                        if ($i == MAX_ITERATIONS) {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                        return round($x,12);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function CHIINV()


        /**
         * CONFIDENCE
         *
         * Returns the confidence interval for a population mean
         *
         * @param       float           $alpha
         * @param       float           $stdDev         Standard Deviation
         * @param       float           $size
         * @return      float
         *
         */
        public static function CONFIDENCE($alpha,$stdDev,$size) {
                $alpha  = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
                $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
                $size   = floor(PHPExcel_Calculation_Functions::flattenSingleValue($size));

                if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
                        if (($alpha <= 0) || ($alpha >= 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($stdDev <= 0) || ($size < 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function CONFIDENCE()


        /**
         * CORREL
         *
         * Returns covariance, the average of the products of deviations for each data point pair.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function CORREL($yValues,$xValues=null) {
                if ((is_null($xValues)) || (!is_array($yValues)) || (!is_array($xValues))) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getCorrelation();
        }       //      function CORREL()


        /**
         * COUNT
         *
         * Counts the number of cells that contain numbers within the list of arguments
         *
         * Excel Function:
         *              COUNT(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      int
         */
        public static function COUNT() {
                // Return value
                $returnValue = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
                foreach ($aArgs as $k => $arg) {
                        if ((is_bool($arg)) &&
                                ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
                                $arg = (integer) $arg;
                        }
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                ++$returnValue;
                        }
                }

                // Return
                return $returnValue;
        }       //      function COUNT()


        /**
         * COUNTA
         *
         * Counts the number of cells that are not empty within the list of arguments
         *
         * Excel Function:
         *              COUNTA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      int
         */
        public static function COUNTA() {
                // Return value
                $returnValue = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a numeric, boolean or string value?
                        if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
                                ++$returnValue;
                        }
                }

                // Return
                return $returnValue;
        }       //      function COUNTA()


        /**
         * COUNTBLANK
         *
         * Counts the number of empty cells within the list of arguments
         *
         * Excel Function:
         *              COUNTBLANK(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      int
         */
        public static function COUNTBLANK() {
                // Return value
                $returnValue = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a blank cell?
                        if ((is_null($arg)) || ((is_string($arg)) && ($arg == ''))) {
                                ++$returnValue;
                        }
                }

                // Return
                return $returnValue;
        }       //      function COUNTBLANK()


        /**
         * COUNTIF
         *
         * Counts the number of cells that contain numbers within the list of arguments
         *
         * Excel Function:
         *              COUNTIF(value1[,value2[, ...]],condition)
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @param       string          $condition              The criteria that defines which cells will be counted.
         * @return      int
         */
        public static function COUNTIF($aArgs,$condition) {
                // Return value
                $returnValue = 0;

                $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
                $condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
                // Loop through arguments
                foreach ($aArgs as $arg) {
                        if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
                        $testCondition = '='.$arg.$condition;
                        if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
                                // Is it a value within our criteria
                                ++$returnValue;
                        }
                }

                // Return
                return $returnValue;
        }       //      function COUNTIF()


        /**
         * COVAR
         *
         * Returns covariance, the average of the products of deviations for each data point pair.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function COVAR($yValues,$xValues) {
                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getCovariance();
        }       //      function COVAR()


        /**
         * CRITBINOM
         *
         * Returns the smallest value for which the cumulative binomial distribution is greater
         *              than or equal to a criterion value
         *
         * See http://support.microsoft.com/kb/828117/ for details of the algorithm used
         *
         * @param       float           $trials                 number of Bernoulli trials
         * @param       float           $probability    probability of a success on each trial
         * @param       float           $alpha                  criterion value
         * @return      int
         *
         * @todo        Warning. This implementation differs from the algorithm detailed on the MS
         *                      web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
         *                      This eliminates a potential endless loop error, but may have an adverse affect on the
         *                      accuracy of the function (although all my tests have so far returned correct results).
         *
         */
        public static function CRITBINOM($trials, $probability, $alpha) {
                $trials                 = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $alpha                  = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);

                if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
                        if ($trials < 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($probability < 0) || ($probability > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($alpha < 0) || ($alpha > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ($alpha <= 0.5) {
                                $t = sqrt(log(1 / ($alpha * $alpha)));
                                $trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
                        } else {
                                $t = sqrt(log(1 / pow(1 - $alpha,2)));
                                $trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
                        }
                        $Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
                        if ($Guess < 0) {
                                $Guess = 0;
                        } elseif ($Guess > $trials) {
                                $Guess = $trials;
                        }

                        $TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
                        $EssentiallyZero = 10e-12;

                        $m = floor($trials * $probability);
                        ++$TotalUnscaledProbability;
                        if ($m == $Guess) { ++$UnscaledPGuess; }
                        if ($m <= $Guess) { ++$UnscaledCumPGuess; }

                        $PreviousValue = 1;
                        $Done = False;
                        $k = $m + 1;
                        while ((!$Done) && ($k <= $trials)) {
                                $CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
                                $TotalUnscaledProbability += $CurrentValue;
                                if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
                                if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
                                if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
                                $PreviousValue = $CurrentValue;
                                ++$k;
                        }

                        $PreviousValue = 1;
                        $Done = False;
                        $k = $m - 1;
                        while ((!$Done) && ($k >= 0)) {
                                $CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
                                $TotalUnscaledProbability += $CurrentValue;
                                if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
                                if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
                                if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
                                $PreviousValue = $CurrentValue;
                                --$k;
                        }

                        $PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
                        $CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;

//                      $CumPGuessMinus1 = $CumPGuess - $PGuess;
                        $CumPGuessMinus1 = $CumPGuess - 1;

                        while (True) {
                                if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
                                        return $Guess;
                                } elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
                                        $PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
                                        $CumPGuessMinus1 = $CumPGuess;
                                        $CumPGuess = $CumPGuess + $PGuessPlus1;
                                        $PGuess = $PGuessPlus1;
                                        ++$Guess;
                                } elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
                                        $PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
                                        $CumPGuess = $CumPGuessMinus1;
                                        $CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
                                        $PGuess = $PGuessMinus1;
                                        --$Guess;
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function CRITBINOM()


        /**
         * DEVSQ
         *
         * Returns the sum of squares of deviations of data points from their sample mean.
         *
         * Excel Function:
         *              DEVSQ(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function DEVSQ() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

                // Return value
                $returnValue = null;

                $aMean = self::AVERAGE($aArgs);
                if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
                        $aCount = -1;
                        foreach ($aArgs as $k => $arg) {
                                // Is it a numeric value?
                                if ((is_bool($arg)) &&
                                        ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
                                        $arg = (integer) $arg;
                                }
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        if (is_null($returnValue)) {
                                                $returnValue = pow(($arg - $aMean),2);
                                        } else {
                                                $returnValue += pow(($arg - $aMean),2);
                                        }
                                        ++$aCount;
                                }
                        }

                        // Return
                        if (is_null($returnValue)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        } else {
                                return $returnValue;
                        }
                }
                return self::NA();
        }       //      function DEVSQ()


        /**
         * EXPONDIST
         *
         *      Returns the exponential distribution. Use EXPONDIST to model the time between events,
         *              such as how long an automated bank teller takes to deliver cash. For example, you can
         *              use EXPONDIST to determine the probability that the process takes at most 1 minute.
         *
         * @param       float           $value                  Value of the function
         * @param       float           $lambda                 The parameter value
         * @param       boolean         $cumulative
         * @return      float
         */
        public static function EXPONDIST($value, $lambda, $cumulative) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $lambda = PHPExcel_Calculation_Functions::flattenSingleValue($lambda);
                $cumulative     = PHPExcel_Calculation_Functions::flattenSingleValue($cumulative);

                if ((is_numeric($value)) && (is_numeric($lambda))) {
                        if (($value < 0) || ($lambda < 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
                                if ($cumulative) {
                                        return 1 - exp(0-$value*$lambda);
                                } else {
                                        return $lambda * exp(0-$value*$lambda);
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function EXPONDIST()


        /**
         * FISHER
         *
         * Returns the Fisher transformation at x. This transformation produces a function that
         *              is normally distributed rather than skewed. Use this function to perform hypothesis
         *              testing on the correlation coefficient.
         *
         * @param       float           $value
         * @return      float
         */
        public static function FISHER($value) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);

                if (is_numeric($value)) {
                        if (($value <= -1) || ($value >= 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return 0.5 * log((1+$value)/(1-$value));
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function FISHER()


        /**
         * FISHERINV
         *
         * Returns the inverse of the Fisher transformation. Use this transformation when
         *              analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
         *              FISHERINV(y) = x.
         *
         * @param       float           $value
         * @return      float
         */
        public static function FISHERINV($value) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);

                if (is_numeric($value)) {
                        return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function FISHERINV()


        /**
         * FORECAST
         *
         * Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
         *
         * @param       float                           Value of X for which we want to find Y
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function FORECAST($xValue,$yValues,$xValues) {
                $xValue = PHPExcel_Calculation_Functions::flattenSingleValue($xValue);
                if (!is_numeric($xValue)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }

                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getValueOfYForX($xValue);
        }       //      function FORECAST()


        /**
         * GAMMADIST
         *
         * Returns the gamma distribution.
         *
         * @param       float           $value                  Value at which you want to evaluate the distribution
         * @param       float           $a                              Parameter to the distribution
         * @param       float           $b                              Parameter to the distribution
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function GAMMADIST($value,$a,$b,$cumulative) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $a              = PHPExcel_Calculation_Functions::flattenSingleValue($a);
                $b              = PHPExcel_Calculation_Functions::flattenSingleValue($b);

                if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
                        if (($value < 0) || ($a <= 0) || ($b <= 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
                                if ($cumulative) {
                                        return self::_incompleteGamma($a,$value / $b) / self::_gamma($a);
                                } else {
                                        return (1 / (pow($b,$a) * self::_gamma($a))) * pow($value,$a-1) * exp(0-($value / $b));
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function GAMMADIST()


        /**
         * GAMMAINV
         *
         * Returns the inverse of the beta distribution.
         *
         * @param       float           $probability    Probability at which you want to evaluate the distribution
         * @param       float           $alpha                  Parameter to the distribution
         * @param       float           $beta                   Parameter to the distribution
         * @return      float
         *
         */
        public static function GAMMAINV($probability,$alpha,$beta) {
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $alpha                  = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
                $beta                   = PHPExcel_Calculation_Functions::flattenSingleValue($beta);

                if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
                        if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }

                        $xLo = 0;
                        $xHi = $alpha * $beta * 5;

                        $x = $xNew = 1;
                        $error = $pdf = 0;
                        $dx     = 1024;
                        $i = 0;

                        while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
                                // Apply Newton-Raphson step
                                $error = self::GAMMADIST($x, $alpha, $beta, True) - $probability;
                                if ($error < 0.0) {
                                        $xLo = $x;
                                } else {
                                        $xHi = $x;
                                }
                                $pdf = self::GAMMADIST($x, $alpha, $beta, False);
                                // Avoid division by zero
                                if ($pdf != 0.0) {
                                        $dx = $error / $pdf;
                                        $xNew = $x - $dx;
                                }
                                // If the NR fails to converge (which for example may be the
                                // case if the initial guess is too rough) we apply a bisection
                                // step to determine a more narrow interval around the root.
                                if (($xNew < $xLo) || ($xNew > $xHi) || ($pdf == 0.0)) {
                                        $xNew = ($xLo + $xHi) / 2;
                                        $dx = $xNew - $x;
                                }
                                $x = $xNew;
                        }
                        if ($i == MAX_ITERATIONS) {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                        return $x;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function GAMMAINV()


        /**
         * GAMMALN
         *
         * Returns the natural logarithm of the gamma function.
         *
         * @param       float           $value
         * @return      float
         */
        public static function GAMMALN($value) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);

                if (is_numeric($value)) {
                        if ($value <= 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return log(self::_gamma($value));
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function GAMMALN()


        /**
         * GEOMEAN
         *
         * Returns the geometric mean of an array or range of positive data. For example, you
         *              can use GEOMEAN to calculate average growth rate given compound interest with
         *              variable rates.
         *
         * Excel Function:
         *              GEOMEAN(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function GEOMEAN() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                $aMean = PHPExcel_Calculation_MathTrig::PRODUCT($aArgs);
                if (is_numeric($aMean) && ($aMean > 0)) {
                        $aCount = self::COUNT($aArgs) ;
                        if (self::MIN($aArgs) > 0) {
                                return pow($aMean, (1 / $aCount));
                        }
                }
                return PHPExcel_Calculation_Functions::NaN();
        }       //      GEOMEAN()


        /**
         * GROWTH
         *
         * Returns values along a predicted emponential trend
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @param       array of mixed          Values of X for which we want to find Y
         * @param       boolean                         A logical value specifying whether to force the intersect to equal 0.
         * @return      array of float
         */
        public static function GROWTH($yValues,$xValues=array(),$newValues=array(),$const=True) {
                $yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
                $xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
                $newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
                $const  = (is_null($const))     ? True :        (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);

                $bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
                if (empty($newValues)) {
                        $newValues = $bestFitExponential->getXValues();
                }

                $returnArray = array();
                foreach($newValues as $xValue) {
                        $returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
                }

                return $returnArray;
        }       //      function GROWTH()


        /**
         * HARMEAN
         *
         * Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
         *              arithmetic mean of reciprocals.
         *
         * Excel Function:
         *              HARMEAN(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function HARMEAN() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::NA();

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                if (self::MIN($aArgs) < 0) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                $aCount = 0;
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                if ($arg <= 0) {
                                        return PHPExcel_Calculation_Functions::NaN();
                                }
                                if (is_null($returnValue)) {
                                        $returnValue = (1 / $arg);
                                } else {
                                        $returnValue += (1 / $arg);
                                }
                                ++$aCount;
                        }
                }

                // Return
                if ($aCount > 0) {
                        return 1 / ($returnValue / $aCount);
                } else {
                        return $returnValue;
                }
        }       //      function HARMEAN()


        /**
         * HYPGEOMDIST
         *
         * Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of
         * sample successes, given the sample size, population successes, and population size.
         *
         * @param       float           $sampleSuccesses                Number of successes in the sample
         * @param       float           $sampleNumber                   Size of the sample
         * @param       float           $populationSuccesses    Number of successes in the population
         * @param       float           $populationNumber               Population size
         * @return      float
         *
         */
        public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber) {
                $sampleSuccesses                = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleSuccesses));
                $sampleNumber                   = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleNumber));
                $populationSuccesses    = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationSuccesses));
                $populationNumber               = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationNumber));

                if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
                        if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return PHPExcel_Calculation_MathTrig::COMBIN($populationSuccesses,$sampleSuccesses) *
                                   PHPExcel_Calculation_MathTrig::COMBIN($populationNumber - $populationSuccesses,$sampleNumber - $sampleSuccesses) /
                                   PHPExcel_Calculation_MathTrig::COMBIN($populationNumber,$sampleNumber);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function HYPGEOMDIST()


        /**
         * INTERCEPT
         *
         * Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function INTERCEPT($yValues,$xValues) {
                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getIntersect();
        }       //      function INTERCEPT()


        /**
         * KURT
         *
         * Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
         * or flatness of a distribution compared with the normal distribution. Positive
         * kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
         * relatively flat distribution.
         *
         * @param       array   Data Series
         * @return      float
         */
        public static function KURT() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
                $mean = self::AVERAGE($aArgs);
                $stdDev = self::STDEV($aArgs);

                if ($stdDev > 0) {
                        $count = $summer = 0;
                        // Loop through arguments
                        foreach ($aArgs as $k => $arg) {
                                if ((is_bool($arg)) &&
                                        (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                                } else {
                                        // Is it a numeric value?
                                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                                $summer += pow((($arg - $mean) / $stdDev),4) ;
                                                ++$count;
                                        }
                                }
                        }

                        // Return
                        if ($count > 3) {
                                return $summer * ($count * ($count+1) / (($count-1) * ($count-2) * ($count-3))) - (3 * pow($count-1,2) / (($count-2) * ($count-3)));
                        }
                }
                return PHPExcel_Calculation_Functions::DIV0();
        }       //      function KURT()


        /**
         * LARGE
         *
         * Returns the nth largest value in a data set. You can use this function to
         *              select a value based on its relative standing.
         *
         * Excel Function:
         *              LARGE(value1[,value2[, ...]],entry)
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @param       int                     $entry                  Position (ordered from the largest) in the array or range of data to return
         * @return      float
         *
         */
        public static function LARGE() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                // Calculate
                $entry = floor(array_pop($aArgs));

                if ((is_numeric($entry)) && (!is_string($entry))) {
                        $mArgs = array();
                        foreach ($aArgs as $arg) {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        $mArgs[] = $arg;
                                }
                        }
                        $count = self::COUNT($mArgs);
                        $entry = floor(--$entry);
                        if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        rsort($mArgs);
                        return $mArgs[$entry];
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function LARGE()


        /**
         * LINEST
         *
         * Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data,
         *              and then returns an array that describes the line.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @param       boolean                         A logical value specifying whether to force the intersect to equal 0.
         * @param       boolean                         A logical value specifying whether to return additional regression statistics.
         * @return      array
         */
        public static function LINEST($yValues, $xValues = NULL, $const = TRUE, $stats = FALSE) {
                $const  = (is_null($const))     ? TRUE :        (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
                $stats  = (is_null($stats))     ? FALSE :       (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
                if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));

                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);


                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return 0;
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
                if ($stats) {
                        return array( array( $bestFitLinear->getSlope(),
                                                                 $bestFitLinear->getSlopeSE(),
                                                                 $bestFitLinear->getGoodnessOfFit(),
                                                                 $bestFitLinear->getF(),
                                                                 $bestFitLinear->getSSRegression(),
                                                           ),
                                                  array( $bestFitLinear->getIntersect(),
                                                                 $bestFitLinear->getIntersectSE(),
                                                                 $bestFitLinear->getStdevOfResiduals(),
                                                                 $bestFitLinear->getDFResiduals(),
                                                                 $bestFitLinear->getSSResiduals()
                                                           )
                                                );
                } else {
                        return array( $bestFitLinear->getSlope(),
                                                  $bestFitLinear->getIntersect()
                                                );
                }
        }       //      function LINEST()


        /**
         * LOGEST
         *
         * Calculates an exponential curve that best fits the X and Y data series,
         *              and then returns an array that describes the line.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @param       boolean                         A logical value specifying whether to force the intersect to equal 0.
         * @param       boolean                         A logical value specifying whether to return additional regression statistics.
         * @return      array
         */
        public static function LOGEST($yValues,$xValues=null,$const=True,$stats=False) {
                $const  = (is_null($const))     ? True :        (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
                $stats  = (is_null($stats))     ? False :       (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
                if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));

                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                foreach($yValues as $value) {
                        if ($value <= 0.0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                }


                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return 1;
                }

                $bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
                if ($stats) {
                        return array( array( $bestFitExponential->getSlope(),
                                                                 $bestFitExponential->getSlopeSE(),
                                                                 $bestFitExponential->getGoodnessOfFit(),
                                                                 $bestFitExponential->getF(),
                                                                 $bestFitExponential->getSSRegression(),
                                                           ),
                                                  array( $bestFitExponential->getIntersect(),
                                                                 $bestFitExponential->getIntersectSE(),
                                                                 $bestFitExponential->getStdevOfResiduals(),
                                                                 $bestFitExponential->getDFResiduals(),
                                                                 $bestFitExponential->getSSResiduals()
                                                           )
                                                );
                } else {
                        return array( $bestFitExponential->getSlope(),
                                                  $bestFitExponential->getIntersect()
                                                );
                }
        }       //      function LOGEST()


        /**
         * LOGINV
         *
         * Returns the inverse of the normal cumulative distribution
         *
         * @param       float           $probability
         * @param       float           $mean
         * @param       float           $stdDev
         * @return      float
         *
         * @todo        Try implementing P J Acklam's refinement algorithm for greater
         *                      accuracy if I can get my head round the mathematics
         *                      (as described at) http://home.online.no/~pjacklam/notes/invnorm/
         */
        public static function LOGINV($probability, $mean, $stdDev) {
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $mean                   = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
                $stdDev                 = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);

                if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
                        if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return exp($mean + $stdDev * self::NORMSINV($probability));
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function LOGINV()


        /**
         * LOGNORMDIST
         *
         * Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed
         * with parameters mean and standard_dev.
         *
         * @param       float           $value
         * @param       float           $mean
         * @param       float           $stdDev
         * @return      float
         */
        public static function LOGNORMDIST($value, $mean, $stdDev) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $mean   = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
                $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);

                if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
                        if (($value <= 0) || ($stdDev <= 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return self::NORMSDIST((log($value) - $mean) / $stdDev);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function LOGNORMDIST()


        /**
         * MAX
         *
         * MAX returns the value of the element of the values passed that has the highest value,
         *              with negative numbers considered smaller than positive numbers.
         *
         * Excel Function:
         *              MAX(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function MAX() {
                // Return value
                $returnValue = null;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                if ((is_null($returnValue)) || ($arg > $returnValue)) {
                                        $returnValue = $arg;
                                }
                        }
                }

                // Return
                if(is_null($returnValue)) {
                        return 0;
                }
                return $returnValue;
        }       //      function MAX()


        /**
         * MAXA
         *
         * Returns the greatest value in a list of arguments, including numbers, text, and logical values
         *
         * Excel Function:
         *              MAXA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function MAXA() {
                // Return value
                $returnValue = null;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
                                if (is_bool($arg)) {
                                        $arg = (integer) $arg;
                                } elseif (is_string($arg)) {
                                        $arg = 0;
                                }
                                if ((is_null($returnValue)) || ($arg > $returnValue)) {
                                        $returnValue = $arg;
                                }
                        }
                }

                // Return
                if(is_null($returnValue)) {
                        return 0;
                }
                return $returnValue;
        }       //      function MAXA()


        /**
         * MAXIF
         *
         * Counts the maximum value within a range of cells that contain numbers within the list of arguments
         *
         * Excel Function:
         *              MAXIF(value1[,value2[, ...]],condition)
         *
         * @access      public
         * @category Mathematical and Trigonometric Functions
         * @param       mixed           $arg,...                Data values
         * @param       string          $condition              The criteria that defines which cells will be checked.
         * @return      float
         */
        public static function MAXIF($aArgs,$condition,$sumArgs = array()) {
                // Return value
                $returnValue = null;

                $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
                $sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
                if (empty($sumArgs)) {
                        $sumArgs = $aArgs;
                }
                $condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
                // Loop through arguments
                foreach ($aArgs as $key => $arg) {
                        if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
                        $testCondition = '='.$arg.$condition;
                        if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
                                if ((is_null($returnValue)) || ($arg > $returnValue)) {
                                        $returnValue = $arg;
                                }
                        }
                }

                // Return
                return $returnValue;
        }       //      function MAXIF()


        /**
         * MEDIAN
         *
         * Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
         *
         * Excel Function:
         *              MEDIAN(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function MEDIAN() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::NaN();

                $mArgs = array();
                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                $mArgs[] = $arg;
                        }
                }

                $mValueCount = count($mArgs);
                if ($mValueCount > 0) {
                        sort($mArgs,SORT_NUMERIC);
                        $mValueCount = $mValueCount / 2;
                        if ($mValueCount == floor($mValueCount)) {
                                $returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2;
                        } else {
                                $mValueCount == floor($mValueCount);
                                $returnValue = $mArgs[$mValueCount];
                        }
                }

                // Return
                return $returnValue;
        }       //      function MEDIAN()


        /**
         * MIN
         *
         * MIN returns the value of the element of the values passed that has the smallest value,
         *              with negative numbers considered smaller than positive numbers.
         *
         * Excel Function:
         *              MIN(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function MIN() {
                // Return value
                $returnValue = null;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                if ((is_null($returnValue)) || ($arg < $returnValue)) {
                                        $returnValue = $arg;
                                }
                        }
                }

                // Return
                if(is_null($returnValue)) {
                        return 0;
                }
                return $returnValue;
        }       //      function MIN()


        /**
         * MINA
         *
         * Returns the smallest value in a list of arguments, including numbers, text, and logical values
         *
         * Excel Function:
         *              MINA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function MINA() {
                // Return value
                $returnValue = null;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
                                if (is_bool($arg)) {
                                        $arg = (integer) $arg;
                                } elseif (is_string($arg)) {
                                        $arg = 0;
                                }
                                if ((is_null($returnValue)) || ($arg < $returnValue)) {
                                        $returnValue = $arg;
                                }
                        }
                }

                // Return
                if(is_null($returnValue)) {
                        return 0;
                }
                return $returnValue;
        }       //      function MINA()


        /**
         * MINIF
         *
         * Returns the minimum value within a range of cells that contain numbers within the list of arguments
         *
         * Excel Function:
         *              MINIF(value1[,value2[, ...]],condition)
         *
         * @access      public
         * @category Mathematical and Trigonometric Functions
         * @param       mixed           $arg,...                Data values
         * @param       string          $condition              The criteria that defines which cells will be checked.
         * @return      float
         */
        public static function MINIF($aArgs,$condition,$sumArgs = array()) {
                // Return value
                $returnValue = null;

                $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
                $sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
                if (empty($sumArgs)) {
                        $sumArgs = $aArgs;
                }
                $condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
                // Loop through arguments
                foreach ($aArgs as $key => $arg) {
                        if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
                        $testCondition = '='.$arg.$condition;
                        if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
                                if ((is_null($returnValue)) || ($arg < $returnValue)) {
                                        $returnValue = $arg;
                                }
                        }
                }

                // Return
                return $returnValue;
        }       //      function MINIF()


        //
        //      Special variant of array_count_values that isn't limited to strings and integers,
        //              but can work with floating point numbers as values
        //
        private static function _modeCalc($data) {
                $frequencyArray = array();
                foreach($data as $datum) {
                        $found = False;
                        foreach($frequencyArray as $key => $value) {
                                if ((string) $value['value'] == (string) $datum) {
                                        ++$frequencyArray[$key]['frequency'];
                                        $found = True;
                                        break;
                                }
                        }
                        if (!$found) {
                                $frequencyArray[] = array('value'               => $datum,
                                                                                  'frequency'   =>      1 );
                        }
                }

                foreach($frequencyArray as $key => $value) {
                        $frequencyList[$key] = $value['frequency'];
                        $valueList[$key] = $value['value'];
                }
                array_multisort($frequencyList, SORT_DESC, $valueList, SORT_ASC, SORT_NUMERIC, $frequencyArray);

                if ($frequencyArray[0]['frequency'] == 1) {
                        return PHPExcel_Calculation_Functions::NA();
                }
                return $frequencyArray[0]['value'];
        }       //      function _modeCalc()


        /**
         * MODE
         *
         * Returns the most frequently occurring, or repetitive, value in an array or range of data
         *
         * Excel Function:
         *              MODE(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function MODE() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::NA();

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                $mArgs = array();
                foreach ($aArgs as $arg) {
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                $mArgs[] = $arg;
                        }
                }

                if (!empty($mArgs)) {
                        return self::_modeCalc($mArgs);
                }

                // Return
                return $returnValue;
        }       //      function MODE()


        /**
         * NEGBINOMDIST
         *
         * Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
         *              there will be number_f failures before the number_s-th success, when the constant
         *              probability of a success is probability_s. This function is similar to the binomial
         *              distribution, except that the number of successes is fixed, and the number of trials is
         *              variable. Like the binomial, trials are assumed to be independent.
         *
         * @param       float           $failures               Number of Failures
         * @param       float           $successes              Threshold number of Successes
         * @param       float           $probability    Probability of success on each trial
         * @return      float
         *
         */
        public static function NEGBINOMDIST($failures, $successes, $probability) {
                $failures               = floor(PHPExcel_Calculation_Functions::flattenSingleValue($failures));
                $successes              = floor(PHPExcel_Calculation_Functions::flattenSingleValue($successes));
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);

                if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
                        if (($failures < 0) || ($successes < 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (($probability < 0) || ($probability > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                                if (($failures + $successes - 1) <= 0) {
                                        return PHPExcel_Calculation_Functions::NaN();
                                }
                        }
                        return (PHPExcel_Calculation_MathTrig::COMBIN($failures + $successes - 1,$successes - 1)) * (pow($probability,$successes)) * (pow(1 - $probability,$failures)) ;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function NEGBINOMDIST()


        /**
         * NORMDIST
         *
         * Returns the normal distribution for the specified mean and standard deviation. This
         * function has a very wide range of applications in statistics, including hypothesis
         * testing.
         *
         * @param       float           $value
         * @param       float           $mean           Mean Value
         * @param       float           $stdDev         Standard Deviation
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function NORMDIST($value, $mean, $stdDev, $cumulative) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $mean   = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
                $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);

                if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
                        if ($stdDev < 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
                                if ($cumulative) {
                                        return 0.5 * (1 + PHPExcel_Calculation_Engineering::_erfVal(($value - $mean) / ($stdDev * sqrt(2))));
                                } else {
                                        return (1 / (SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean,2) / (2 * ($stdDev * $stdDev))));
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function NORMDIST()


        /**
         * NORMINV
         *
         * Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
         *
         * @param       float           $value
         * @param       float           $mean           Mean Value
         * @param       float           $stdDev         Standard Deviation
         * @return      float
         *
         */
        public static function NORMINV($probability,$mean,$stdDev) {
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $mean                   = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
                $stdDev                 = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);

                if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
                        if (($probability < 0) || ($probability > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ($stdDev < 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return (self::_inverse_ncdf($probability) * $stdDev) + $mean;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function NORMINV()


        /**
         * NORMSDIST
         *
         * Returns the standard normal cumulative distribution function. The distribution has
         * a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
         * table of standard normal curve areas.
         *
         * @param       float           $value
         * @return      float
         */
        public static function NORMSDIST($value) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);

                return self::NORMDIST($value, 0, 1, True);
        }       //      function NORMSDIST()


        /**
         * NORMSINV
         *
         * Returns the inverse of the standard normal cumulative distribution
         *
         * @param       float           $value
         * @return      float
         */
        public static function NORMSINV($value) {
                return self::NORMINV($value, 0, 1);
        }       //      function NORMSINV()


        /**
         * PERCENTILE
         *
         * Returns the nth percentile of values in a range..
         *
         * Excel Function:
         *              PERCENTILE(value1[,value2[, ...]],entry)
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @param       float           $entry                  Percentile value in the range 0..1, inclusive.
         * @return      float
         */
        public static function PERCENTILE() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                // Calculate
                $entry = array_pop($aArgs);

                if ((is_numeric($entry)) && (!is_string($entry))) {
                        if (($entry < 0) || ($entry > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        $mArgs = array();
                        foreach ($aArgs as $arg) {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        $mArgs[] = $arg;
                                }
                        }
                        $mValueCount = count($mArgs);
                        if ($mValueCount > 0) {
                                sort($mArgs);
                                $count = self::COUNT($mArgs);
                                $index = $entry * ($count-1);
                                $iBase = floor($index);
                                if ($index == $iBase) {
                                        return $mArgs[$index];
                                } else {
                                        $iNext = $iBase + 1;
                                        $iProportion = $index - $iBase;
                                        return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion) ;
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function PERCENTILE()


        /**
         * PERCENTRANK
         *
         * Returns the rank of a value in a data set as a percentage of the data set.
         *
         * @param       array of number         An array of, or a reference to, a list of numbers.
         * @param       number                          The number whose rank you want to find.
         * @param       number                          The number of significant digits for the returned percentage value.
         * @return      float
         */
        public static function PERCENTRANK($valueSet,$value,$significance=3) {
                $valueSet       = PHPExcel_Calculation_Functions::flattenArray($valueSet);
                $value          = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $significance   = (is_null($significance))      ? 3 :   (integer) PHPExcel_Calculation_Functions::flattenSingleValue($significance);

                foreach($valueSet as $key => $valueEntry) {
                        if (!is_numeric($valueEntry)) {
                                unset($valueSet[$key]);
                        }
                }
                sort($valueSet,SORT_NUMERIC);
                $valueCount = count($valueSet);
                if ($valueCount == 0) {
                        return PHPExcel_Calculation_Functions::NaN();
                }

                $valueAdjustor = $valueCount - 1;
                if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) {
                        return PHPExcel_Calculation_Functions::NA();
                }

                $pos = array_search($value,$valueSet);
                if ($pos === False) {
                        $pos = 0;
                        $testValue = $valueSet[0];
                        while ($testValue < $value) {
                                $testValue = $valueSet[++$pos];
                        }
                        --$pos;
                        $pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos]));
                }

                return round($pos / $valueAdjustor,$significance);
        }       //      function PERCENTRANK()


        /**
         * PERMUT
         *
         * Returns the number of permutations for a given number of objects that can be
         *              selected from number objects. A permutation is any set or subset of objects or
         *              events where internal order is significant. Permutations are different from
         *              combinations, for which the internal order is not significant. Use this function
         *              for lottery-style probability calculations.
         *
         * @param       int             $numObjs        Number of different objects
         * @param       int             $numInSet       Number of objects in each permutation
         * @return      int             Number of permutations
         */
        public static function PERMUT($numObjs,$numInSet) {
                $numObjs        = PHPExcel_Calculation_Functions::flattenSingleValue($numObjs);
                $numInSet       = PHPExcel_Calculation_Functions::flattenSingleValue($numInSet);

                if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
                        $numInSet = floor($numInSet);
                        if ($numObjs < $numInSet) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return round(PHPExcel_Calculation_MathTrig::FACT($numObjs) / PHPExcel_Calculation_MathTrig::FACT($numObjs - $numInSet));
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function PERMUT()


        /**
         * POISSON
         *
         * Returns the Poisson distribution. A common application of the Poisson distribution
         * is predicting the number of events over a specific time, such as the number of
         * cars arriving at a toll plaza in 1 minute.
         *
         * @param       float           $value
         * @param       float           $mean           Mean Value
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function POISSON($value, $mean, $cumulative) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $mean   = PHPExcel_Calculation_Functions::flattenSingleValue($mean);

                if ((is_numeric($value)) && (is_numeric($mean))) {
                        if (($value <= 0) || ($mean <= 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
                                if ($cumulative) {
                                        $summer = 0;
                                        for ($i = 0; $i <= floor($value); ++$i) {
                                                $summer += pow($mean,$i) / PHPExcel_Calculation_MathTrig::FACT($i);
                                        }
                                        return exp(0-$mean) * $summer;
                                } else {
                                        return (exp(0-$mean) * pow($mean,$value)) / PHPExcel_Calculation_MathTrig::FACT($value);
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function POISSON()


        /**
         * QUARTILE
         *
         * Returns the quartile of a data set.
         *
         * Excel Function:
         *              QUARTILE(value1[,value2[, ...]],entry)
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @param       int                     $entry                  Quartile value in the range 1..3, inclusive.
         * @return      float
         */
        public static function QUARTILE() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                // Calculate
                $entry = floor(array_pop($aArgs));

                if ((is_numeric($entry)) && (!is_string($entry))) {
                        $entry /= 4;
                        if (($entry < 0) || ($entry > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return self::PERCENTILE($aArgs,$entry);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function QUARTILE()


        /**
         * RANK
         *
         * Returns the rank of a number in a list of numbers.
         *
         * @param       number                          The number whose rank you want to find.
         * @param       array of number         An array of, or a reference to, a list of numbers.
         * @param       mixed                           Order to sort the values in the value set
         * @return      float
         */
        public static function RANK($value,$valueSet,$order=0) {
                $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
                $order  = (is_null($order))     ? 0 :   (integer) PHPExcel_Calculation_Functions::flattenSingleValue($order);

                foreach($valueSet as $key => $valueEntry) {
                        if (!is_numeric($valueEntry)) {
                                unset($valueSet[$key]);
                        }
                }

                if ($order == 0) {
                        rsort($valueSet,SORT_NUMERIC);
                } else {
                        sort($valueSet,SORT_NUMERIC);
                }
                $pos = array_search($value,$valueSet);
                if ($pos === False) {
                        return PHPExcel_Calculation_Functions::NA();
                }

                return ++$pos;
        }       //      function RANK()


        /**
         * RSQ
         *
         * Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function RSQ($yValues,$xValues) {
                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getGoodnessOfFit();
        }       //      function RSQ()


        /**
         * SKEW
         *
         * Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
         * of a distribution around its mean. Positive skewness indicates a distribution with an
         * asymmetric tail extending toward more positive values. Negative skewness indicates a
         * distribution with an asymmetric tail extending toward more negative values.
         *
         * @param       array   Data Series
         * @return      float
         */
        public static function SKEW() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
                $mean = self::AVERAGE($aArgs);
                $stdDev = self::STDEV($aArgs);

                $count = $summer = 0;
                // Loop through arguments
                foreach ($aArgs as $k => $arg) {
                        if ((is_bool($arg)) &&
                                (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                        } else {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        $summer += pow((($arg - $mean) / $stdDev),3) ;
                                        ++$count;
                                }
                        }
                }

                // Return
                if ($count > 2) {
                        return $summer * ($count / (($count-1) * ($count-2)));
                }
                return PHPExcel_Calculation_Functions::DIV0();
        }       //      function SKEW()


        /**
         * SLOPE
         *
         * Returns the slope of the linear regression line through data points in known_y's and known_x's.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function SLOPE($yValues,$xValues) {
                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getSlope();
        }       //      function SLOPE()


        /**
         * SMALL
         *
         * Returns the nth smallest value in a data set. You can use this function to
         *              select a value based on its relative standing.
         *
         * Excel Function:
         *              SMALL(value1[,value2[, ...]],entry)
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @param       int                     $entry                  Position (ordered from the smallest) in the array or range of data to return
         * @return      float
         */
        public static function SMALL() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                // Calculate
                $entry = array_pop($aArgs);

                if ((is_numeric($entry)) && (!is_string($entry))) {
                        $mArgs = array();
                        foreach ($aArgs as $arg) {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        $mArgs[] = $arg;
                                }
                        }
                        $count = self::COUNT($mArgs);
                        $entry = floor(--$entry);
                        if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        sort($mArgs);
                        return $mArgs[$entry];
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function SMALL()


        /**
         * STANDARDIZE
         *
         * Returns a normalized value from a distribution characterized by mean and standard_dev.
         *
         * @param       float   $value          Value to normalize
         * @param       float   $mean           Mean Value
         * @param       float   $stdDev         Standard Deviation
         * @return      float   Standardized value
         */
        public static function STANDARDIZE($value,$mean,$stdDev) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $mean   = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
                $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);

                if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
                        if ($stdDev <= 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        return ($value - $mean) / $stdDev ;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function STANDARDIZE()


        /**
         * STDEV
         *
         * Estimates standard deviation based on a sample. The standard deviation is a measure of how
         *              widely values are dispersed from the average value (the mean).
         *
         * Excel Function:
         *              STDEV(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function STDEV() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

                // Return value
                $returnValue = null;

                $aMean = self::AVERAGE($aArgs);
                if (!is_null($aMean)) {
                        $aCount = -1;
                        foreach ($aArgs as $k => $arg) {
                                if ((is_bool($arg)) &&
                                        ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
                                        $arg = (integer) $arg;
                                }
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        if (is_null($returnValue)) {
                                                $returnValue = pow(($arg - $aMean),2);
                                        } else {
                                                $returnValue += pow(($arg - $aMean),2);
                                        }
                                        ++$aCount;
                                }
                        }

                        // Return
                        if (($aCount > 0) && ($returnValue >= 0)) {
                                return sqrt($returnValue / $aCount);
                        }
                }
                return PHPExcel_Calculation_Functions::DIV0();
        }       //      function STDEV()


        /**
         * STDEVA
         *
         * Estimates standard deviation based on a sample, including numbers, text, and logical values
         *
         * Excel Function:
         *              STDEVA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function STDEVA() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

                // Return value
                $returnValue = null;

                $aMean = self::AVERAGEA($aArgs);
                if (!is_null($aMean)) {
                        $aCount = -1;
                        foreach ($aArgs as $k => $arg) {
                                if ((is_bool($arg)) &&
                                        (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                                } else {
                                        // Is it a numeric value?
                                        if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
                                                if (is_bool($arg)) {
                                                        $arg = (integer) $arg;
                                                } elseif (is_string($arg)) {
                                                        $arg = 0;
                                                }
                                                if (is_null($returnValue)) {
                                                        $returnValue = pow(($arg - $aMean),2);
                                                } else {
                                                        $returnValue += pow(($arg - $aMean),2);
                                                }
                                                ++$aCount;
                                        }
                                }
                        }

                        // Return
                        if (($aCount > 0) && ($returnValue >= 0)) {
                                return sqrt($returnValue / $aCount);
                        }
                }
                return PHPExcel_Calculation_Functions::DIV0();
        }       //      function STDEVA()


        /**
         * STDEVP
         *
         * Calculates standard deviation based on the entire population
         *
         * Excel Function:
         *              STDEVP(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function STDEVP() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

                // Return value
                $returnValue = null;

                $aMean = self::AVERAGE($aArgs);
                if (!is_null($aMean)) {
                        $aCount = 0;
                        foreach ($aArgs as $k => $arg) {
                                if ((is_bool($arg)) &&
                                        ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
                                        $arg = (integer) $arg;
                                }
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        if (is_null($returnValue)) {
                                                $returnValue = pow(($arg - $aMean),2);
                                        } else {
                                                $returnValue += pow(($arg - $aMean),2);
                                        }
                                        ++$aCount;
                                }
                        }

                        // Return
                        if (($aCount > 0) && ($returnValue >= 0)) {
                                return sqrt($returnValue / $aCount);
                        }
                }
                return PHPExcel_Calculation_Functions::DIV0();
        }       //      function STDEVP()


        /**
         * STDEVPA
         *
         * Calculates standard deviation based on the entire population, including numbers, text, and logical values
         *
         * Excel Function:
         *              STDEVPA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function STDEVPA() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

                // Return value
                $returnValue = null;

                $aMean = self::AVERAGEA($aArgs);
                if (!is_null($aMean)) {
                        $aCount = 0;
                        foreach ($aArgs as $k => $arg) {
                                if ((is_bool($arg)) &&
                                        (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                                } else {
                                        // Is it a numeric value?
                                        if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
                                                if (is_bool($arg)) {
                                                        $arg = (integer) $arg;
                                                } elseif (is_string($arg)) {
                                                        $arg = 0;
                                                }
                                                if (is_null($returnValue)) {
                                                        $returnValue = pow(($arg - $aMean),2);
                                                } else {
                                                        $returnValue += pow(($arg - $aMean),2);
                                                }
                                                ++$aCount;
                                        }
                                }
                        }

                        // Return
                        if (($aCount > 0) && ($returnValue >= 0)) {
                                return sqrt($returnValue / $aCount);
                        }
                }
                return PHPExcel_Calculation_Functions::DIV0();
        }       //      function STDEVPA()


        /**
         * STEYX
         *
         * Returns the standard error of the predicted y-value for each x in the regression.
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @return      float
         */
        public static function STEYX($yValues,$xValues) {
                if (!self::_checkTrendArrays($yValues,$xValues)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $yValueCount = count($yValues);
                $xValueCount = count($xValues);

                if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
                        return PHPExcel_Calculation_Functions::NA();
                } elseif ($yValueCount == 1) {
                        return PHPExcel_Calculation_Functions::DIV0();
                }

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
                return $bestFitLinear->getStdevOfResiduals();
        }       //      function STEYX()


        /**
         * TDIST
         *
         * Returns the probability of Student's T distribution.
         *
         * @param       float           $value                  Value for the function
         * @param       float           $degrees                degrees of freedom
         * @param       float           $tails                  number of tails (1 or 2)
         * @return      float
         */
        public static function TDIST($value, $degrees, $tails) {
                $value          = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $degrees        = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
                $tails          = floor(PHPExcel_Calculation_Functions::flattenSingleValue($tails));

                if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
                        if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        //      tdist, which finds the probability that corresponds to a given value
                        //      of t with k degrees of freedom. This algorithm is translated from a
                        //      pascal function on p81 of "Statistical Computing in Pascal" by D
                        //      Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
                        //      London). The above Pascal algorithm is itself a translation of the
                        //      fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
                        //      Laboratory as reported in (among other places) "Applied Statistics
                        //      Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
                        //      Horwood Ltd.; W. Sussex, England).
                        $tterm = $degrees;
                        $ttheta = atan2($value,sqrt($tterm));
                        $tc = cos($ttheta);
                        $ts = sin($ttheta);
                        $tsum = 0;

                        if (($degrees % 2) == 1) {
                                $ti = 3;
                                $tterm = $tc;
                        } else {
                                $ti = 2;
                                $tterm = 1;
                        }

                        $tsum = $tterm;
                        while ($ti < $degrees) {
                                $tterm *= $tc * $tc * ($ti - 1) / $ti;
                                $tsum += $tterm;
                                $ti += 2;
                        }
                        $tsum *= $ts;
                        if (($degrees % 2) == 1) { $tsum = M_2DIVPI * ($tsum + $ttheta); }
                        $tValue = 0.5 * (1 + $tsum);
                        if ($tails == 1) {
                                return 1 - abs($tValue);
                        } else {
                                return 1 - abs((1 - $tValue) - $tValue);
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function TDIST()


        /**
         * TINV
         *
         * Returns the one-tailed probability of the chi-squared distribution.
         *
         * @param       float           $probability    Probability for the function
         * @param       float           $degrees                degrees of freedom
         * @return      float
         */
        public static function TINV($probability, $degrees) {
                $probability    = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
                $degrees                = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));

                if ((is_numeric($probability)) && (is_numeric($degrees))) {
                        $xLo = 100;
                        $xHi = 0;

                        $x = $xNew = 1;
                        $dx     = 1;
                        $i = 0;

                        while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
                                // Apply Newton-Raphson step
                                $result = self::TDIST($x, $degrees, 2);
                                $error = $result - $probability;
                                if ($error == 0.0) {
                                        $dx = 0;
                                } elseif ($error < 0.0) {
                                        $xLo = $x;
                                } else {
                                        $xHi = $x;
                                }
                                // Avoid division by zero
                                if ($result != 0.0) {
                                        $dx = $error / $result;
                                        $xNew = $x - $dx;
                                }
                                // If the NR fails to converge (which for example may be the
                                // case if the initial guess is too rough) we apply a bisection
                                // step to determine a more narrow interval around the root.
                                if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
                                        $xNew = ($xLo + $xHi) / 2;
                                        $dx = $xNew - $x;
                                }
                                $x = $xNew;
                        }
                        if ($i == MAX_ITERATIONS) {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                        return round($x,12);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function TINV()


        /**
         * TREND
         *
         * Returns values along a linear trend
         *
         * @param       array of mixed          Data Series Y
         * @param       array of mixed          Data Series X
         * @param       array of mixed          Values of X for which we want to find Y
         * @param       boolean                         A logical value specifying whether to force the intersect to equal 0.
         * @return      array of float
         */
        public static function TREND($yValues,$xValues=array(),$newValues=array(),$const=True) {
                $yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
                $xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
                $newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
                $const  = (is_null($const))     ? True :        (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);

                $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
                if (empty($newValues)) {
                        $newValues = $bestFitLinear->getXValues();
                }

                $returnArray = array();
                foreach($newValues as $xValue) {
                        $returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
                }

                return $returnArray;
        }       //      function TREND()


        /**
         * TRIMMEAN
         *
         * Returns the mean of the interior of a data set. TRIMMEAN calculates the mean
         *              taken by excluding a percentage of data points from the top and bottom tails
         *              of a data set.
         *
         * Excel Function:
         *              TRIMEAN(value1[,value2[, ...]],$discard)
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @param       float           $discard                Percentage to discard
         * @return      float
         */
        public static function TRIMMEAN() {
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

                // Calculate
                $percent = array_pop($aArgs);

                if ((is_numeric($percent)) && (!is_string($percent))) {
                        if (($percent < 0) || ($percent > 1)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        $mArgs = array();
                        foreach ($aArgs as $arg) {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) && (!is_string($arg))) {
                                        $mArgs[] = $arg;
                                }
                        }
                        $discard = floor(self::COUNT($mArgs) * $percent / 2);
                        sort($mArgs);
                        for ($i=0; $i < $discard; ++$i) {
                                array_pop($mArgs);
                                array_shift($mArgs);
                        }
                        return self::AVERAGE($mArgs);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function TRIMMEAN()


        /**
         * VARFunc
         *
         * Estimates variance based on a sample.
         *
         * Excel Function:
         *              VAR(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function VARFunc() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::DIV0();

                $summerA = $summerB = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                $aCount = 0;
                foreach ($aArgs as $arg) {
                        if (is_bool($arg)) { $arg = (integer) $arg; }
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                $summerA += ($arg * $arg);
                                $summerB += $arg;
                                ++$aCount;
                        }
                }

                // Return
                if ($aCount > 1) {
                        $summerA *= $aCount;
                        $summerB *= $summerB;
                        $returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
                }
                return $returnValue;
        }       //      function VARFunc()


        /**
         * VARA
         *
         * Estimates variance based on a sample, including numbers, text, and logical values
         *
         * Excel Function:
         *              VARA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function VARA() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::DIV0();

                $summerA = $summerB = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
                $aCount = 0;
                foreach ($aArgs as $k => $arg) {
                        if ((is_string($arg)) &&
                                (PHPExcel_Calculation_Functions::isValue($k))) {
                                return PHPExcel_Calculation_Functions::VALUE();
                        } elseif ((is_string($arg)) &&
                                (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                        } else {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
                                        if (is_bool($arg)) {
                                                $arg = (integer) $arg;
                                        } elseif (is_string($arg)) {
                                                $arg = 0;
                                        }
                                        $summerA += ($arg * $arg);
                                        $summerB += $arg;
                                        ++$aCount;
                                }
                        }
                }

                // Return
                if ($aCount > 1) {
                        $summerA *= $aCount;
                        $summerB *= $summerB;
                        $returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
                }
                return $returnValue;
        }       //      function VARA()


        /**
         * VARP
         *
         * Calculates variance based on the entire population
         *
         * Excel Function:
         *              VARP(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function VARP() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::DIV0();

                $summerA = $summerB = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                $aCount = 0;
                foreach ($aArgs as $arg) {
                        if (is_bool($arg)) { $arg = (integer) $arg; }
                        // Is it a numeric value?
                        if ((is_numeric($arg)) && (!is_string($arg))) {
                                $summerA += ($arg * $arg);
                                $summerB += $arg;
                                ++$aCount;
                        }
                }

                // Return
                if ($aCount > 0) {
                        $summerA *= $aCount;
                        $summerB *= $summerB;
                        $returnValue = ($summerA - $summerB) / ($aCount * $aCount);
                }
                return $returnValue;
        }       //      function VARP()


        /**
         * VARPA
         *
         * Calculates variance based on the entire population, including numbers, text, and logical values
         *
         * Excel Function:
         *              VARPA(value1[,value2[, ...]])
         *
         * @access      public
         * @category Statistical Functions
         * @param       mixed           $arg,...                Data values
         * @return      float
         */
        public static function VARPA() {
                // Return value
                $returnValue = PHPExcel_Calculation_Functions::DIV0();

                $summerA = $summerB = 0;

                // Loop through arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
                $aCount = 0;
                foreach ($aArgs as $k => $arg) {
                        if ((is_string($arg)) &&
                                (PHPExcel_Calculation_Functions::isValue($k))) {
                                return PHPExcel_Calculation_Functions::VALUE();
                        } elseif ((is_string($arg)) &&
                                (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
                        } else {
                                // Is it a numeric value?
                                if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
                                        if (is_bool($arg)) {
                                                $arg = (integer) $arg;
                                        } elseif (is_string($arg)) {
                                                $arg = 0;
                                        }
                                        $summerA += ($arg * $arg);
                                        $summerB += $arg;
                                        ++$aCount;
                                }
                        }
                }

                // Return
                if ($aCount > 0) {
                        $summerA *= $aCount;
                        $summerB *= $summerB;
                        $returnValue = ($summerA - $summerB) / ($aCount * $aCount);
                }
                return $returnValue;
        }       //      function VARPA()


        /**
         * WEIBULL
         *
         * Returns the Weibull distribution. Use this distribution in reliability
         * analysis, such as calculating a device's mean time to failure.
         *
         * @param       float           $value
         * @param       float           $alpha          Alpha Parameter
         * @param       float           $beta           Beta Parameter
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function WEIBULL($value, $alpha, $beta, $cumulative) {
                $value  = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $alpha  = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
                $beta   = PHPExcel_Calculation_Functions::flattenSingleValue($beta);

                if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
                        if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
                                if ($cumulative) {
                                        return 1 - exp(0 - pow($value / $beta,$alpha));
                                } else {
                                        return ($alpha / pow($beta,$alpha)) * pow($value,$alpha - 1) * exp(0 - pow($value / $beta,$alpha));
                                }
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function WEIBULL()


        /**
         * ZTEST
         *
         * Returns the Weibull distribution. Use this distribution in reliability
         * analysis, such as calculating a device's mean time to failure.
         *
         * @param       float           $dataSet
         * @param       float           $m0             Alpha Parameter
         * @param       float           $sigma  Beta Parameter
         * @param       boolean         $cumulative
         * @return      float
         *
         */
        public static function ZTEST($dataSet, $m0, $sigma = NULL) {
                $dataSet        = PHPExcel_Calculation_Functions::flattenArrayIndexed($dataSet);
                $m0                     = PHPExcel_Calculation_Functions::flattenSingleValue($m0);
                $sigma          = PHPExcel_Calculation_Functions::flattenSingleValue($sigma);

                if (is_null($sigma)) {
                        $sigma = self::STDEV($dataSet);
                }
                $n = count($dataSet);

                return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0)/($sigma/SQRT($n)));
        }       //      function ZTEST()

}       //      class PHPExcel_Calculation_Statistical