Normal.php

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<?php

namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;

use PhpOffice\PhpSpreadsheet\Calculation\Engineering;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;

class Normal
{
    public const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;

    public static function distribution($value, $mean, $stdDev, $cumulative)
    {
        $value = Functions::flattenSingleValue($value);
        $mean = Functions::flattenSingleValue($mean);
        $stdDev = Functions::flattenSingleValue($stdDev);

        try {
            $value = DistributionValidations::validateFloat($value);
            $mean = DistributionValidations::validateFloat($mean);
            $stdDev = DistributionValidations::validateFloat($stdDev);
            $cumulative = DistributionValidations::validateBool($cumulative);
        } catch (Exception $e) {
            return $e->getMessage();
        }

        if ($stdDev < 0) {
            return Functions::NAN();
        }

        if ($cumulative) {
            return 0.5 * (1 + Engineering\Erf::erfValue(($value - $mean) / ($stdDev * sqrt(2))));
        }

        return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (($value - $mean) ** 2 / (2 * ($stdDev * $stdDev))));
    }

    public static function inverse($probability, $mean, $stdDev)
    {
        $probability = Functions::flattenSingleValue($probability);
        $mean = Functions::flattenSingleValue($mean);
        $stdDev = Functions::flattenSingleValue($stdDev);

        try {
            $probability = DistributionValidations::validateProbability($probability);
            $mean = DistributionValidations::validateFloat($mean);
            $stdDev = DistributionValidations::validateFloat($stdDev);
        } catch (Exception $e) {
            return $e->getMessage();
        }

        if ($stdDev < 0) {
            return Functions::NAN();
        }

        return (self::inverseNcdf($probability) * $stdDev) + $mean;
    }

    /*
     *                                inverse_ncdf.php
     *                            -------------------
     *    begin                : Friday, January 16, 2004
     *    copyright            : (C) 2004 Michael Nickerson
     *    email                : nickersonm@yahoo.com
     *
     */
    private static function inverseNcdf($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 = [
            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 = [
            1 => -5.447609879822406e+01,
            2 => 1.615858368580409e+02,
            3 => -1.556989798598866e+02,
            4 => 6.680131188771972e+01,
            5 => -1.328068155288572e+01,
        ];

        static $c = [
            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 = [
            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_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);
        }

        //    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);
    }
}