<?php
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namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
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use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
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use PhpOffice\PhpSpreadsheet\Calculation\Engineering;
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use PhpOffice\PhpSpreadsheet\Calculation\Exception;
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use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
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class Normal
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{
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use ArrayEnabled;
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public const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;
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/**
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* NORMDIST.
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*
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* Returns the normal distribution for the specified mean and standard deviation. This
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* function has a very wide range of applications in statistics, including hypothesis
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* testing.
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*
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* @param mixed $value Float value for which we want the probability
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* Or can be an array of values
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* @param mixed $mean Mean value as a float
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* Or can be an array of values
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* @param mixed $stdDev Standard Deviation as a float
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* Or can be an array of values
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* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
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* Or can be an array of values
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*
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* @return array|float|string The result, or a string containing an error
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* If an array of numbers is passed as an argument, then the returned result will also be an array
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* with the same dimensions
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*/
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public static function distribution(mixed $value, mixed $mean, mixed $stdDev, mixed $cumulative): array|string|float
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{
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if (is_array($value) || is_array($mean) || is_array($stdDev) || is_array($cumulative)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $mean, $stdDev, $cumulative);
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}
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try {
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$value = DistributionValidations::validateFloat($value);
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$mean = DistributionValidations::validateFloat($mean);
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$stdDev = DistributionValidations::validateFloat($stdDev);
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$cumulative = DistributionValidations::validateBool($cumulative);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if ($stdDev < 0) {
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return ExcelError::NAN();
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}
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if ($cumulative) {
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return 0.5 * (1 + Engineering\Erf::erfValue(($value - $mean) / ($stdDev * sqrt(2))));
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}
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return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (($value - $mean) ** 2 / (2 * ($stdDev * $stdDev))));
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}
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/**
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* NORMINV.
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*
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* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
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*
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* @param mixed $probability Float probability for which we want the value
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* Or can be an array of values
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* @param mixed $mean Mean Value as a float
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* Or can be an array of values
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* @param mixed $stdDev Standard Deviation as a float
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* Or can be an array of values
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*
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* @return array|float|string The result, or a string containing an error
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* If an array of numbers is passed as an argument, then the returned result will also be an array
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* with the same dimensions
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*/
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public static function inverse(mixed $probability, mixed $mean, mixed $stdDev): array|string|float
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{
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if (is_array($probability) || is_array($mean) || is_array($stdDev)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $mean, $stdDev);
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}
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try {
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$probability = DistributionValidations::validateProbability($probability);
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$mean = DistributionValidations::validateFloat($mean);
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$stdDev = DistributionValidations::validateFloat($stdDev);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if ($stdDev < 0) {
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return ExcelError::NAN();
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}
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return (self::inverseNcdf($probability) * $stdDev) + $mean;
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}
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/*
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* inverse_ncdf.php
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* -------------------
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* begin : Friday, January 16, 2004
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* copyright : (C) 2004 Michael Nickerson
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* email : nickersonm@yahoo.com
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*
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*/
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private static function inverseNcdf(float $p): float
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{
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// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
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// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
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// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
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// I have not checked the accuracy of this implementation. Be aware that PHP
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// will truncate the coeficcients to 14 digits.
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// You have permission to use and distribute this function freely for
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// whatever purpose you want, but please show common courtesy and give credit
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// where credit is due.
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// Input paramater is $p - probability - where 0 < p < 1.
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// Coefficients in rational approximations
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static $a = [
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1 => -3.969683028665376e+01,
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2 => 2.209460984245205e+02,
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3 => -2.759285104469687e+02,
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4 => 1.383577518672690e+02,
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5 => -3.066479806614716e+01,
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6 => 2.506628277459239e+00,
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];
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static $b = [
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1 => -5.447609879822406e+01,
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2 => 1.615858368580409e+02,
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3 => -1.556989798598866e+02,
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4 => 6.680131188771972e+01,
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5 => -1.328068155288572e+01,
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];
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static $c = [
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1 => -7.784894002430293e-03,
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2 => -3.223964580411365e-01,
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3 => -2.400758277161838e+00,
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4 => -2.549732539343734e+00,
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5 => 4.374664141464968e+00,
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6 => 2.938163982698783e+00,
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];
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static $d = [
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1 => 7.784695709041462e-03,
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2 => 3.224671290700398e-01,
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3 => 2.445134137142996e+00,
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4 => 3.754408661907416e+00,
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];
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// Define lower and upper region break-points.
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$p_low = 0.02425; //Use lower region approx. below this
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$p_high = 1 - $p_low; //Use upper region approx. above this
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if (0 < $p && $p < $p_low) {
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// Rational approximation for lower region.
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$q = sqrt(-2 * log($p));
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return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6])
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/ (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
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} elseif ($p_high < $p && $p < 1) {
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// Rational approximation for upper region.
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$q = sqrt(-2 * log(1 - $p));
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return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6])
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/ (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
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}
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// Rational approximation for central region.
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$q = $p - 0.5;
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$r = $q * $q;
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return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q
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/ ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
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}
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}
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