<?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\Exception;
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use PhpOffice\PhpSpreadsheet\Calculation\Functions;
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use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
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class Beta
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{
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use ArrayEnabled;
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private const MAX_ITERATIONS = 256;
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private const LOG_GAMMA_X_MAX_VALUE = 2.55e305;
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private const XMININ = 2.23e-308;
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/**
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* BETADIST.
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*
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* Returns the beta distribution.
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*
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* @param mixed $value Float value at which you want to evaluate the distribution
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* Or can be an array of values
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* @param mixed $alpha Parameter to the distribution as a float
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* Or can be an array of values
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* @param mixed $beta Parameter to the distribution as a float
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* Or can be an array of values
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* @param mixed $rMin as an float
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* Or can be an array of values
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* @param mixed $rMax as an float
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* Or can be an array of values
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*
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* @return array|float|string 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 $alpha, mixed $beta, mixed $rMin = 0.0, mixed $rMax = 1.0): array|string|float
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{
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if (is_array($value) || is_array($alpha) || is_array($beta) || is_array($rMin) || is_array($rMax)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $alpha, $beta, $rMin, $rMax);
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}
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$rMin = $rMin ?? 0.0;
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$rMax = $rMax ?? 1.0;
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try {
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$value = DistributionValidations::validateFloat($value);
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$alpha = DistributionValidations::validateFloat($alpha);
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$beta = DistributionValidations::validateFloat($beta);
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$rMax = DistributionValidations::validateFloat($rMax);
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$rMin = DistributionValidations::validateFloat($rMin);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if ($rMin > $rMax) {
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$tmp = $rMin;
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$rMin = $rMax;
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$rMax = $tmp;
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}
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if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
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return ExcelError::NAN();
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}
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$value -= $rMin;
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$value /= ($rMax - $rMin);
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return self::incompleteBeta($value, $alpha, $beta);
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}
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/**
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* BETAINV.
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*
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* Returns the inverse of the Beta distribution.
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*
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* @param mixed $probability Float probability at which you want to evaluate the distribution
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* Or can be an array of values
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* @param mixed $alpha Parameter to the distribution as a float
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* Or can be an array of values
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* @param mixed $beta Parameter to the distribution as a float
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* Or can be an array of values
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* @param mixed $rMin Minimum value as a float
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* Or can be an array of values
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* @param mixed $rMax Maximum value 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 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 $alpha, mixed $beta, mixed $rMin = 0.0, mixed $rMax = 1.0): array|string|float
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{
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if (is_array($probability) || is_array($alpha) || is_array($beta) || is_array($rMin) || is_array($rMax)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $alpha, $beta, $rMin, $rMax);
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}
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$rMin = $rMin ?? 0.0;
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$rMax = $rMax ?? 1.0;
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try {
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$probability = DistributionValidations::validateProbability($probability);
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$alpha = DistributionValidations::validateFloat($alpha);
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$beta = DistributionValidations::validateFloat($beta);
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$rMax = DistributionValidations::validateFloat($rMax);
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$rMin = DistributionValidations::validateFloat($rMin);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if ($rMin > $rMax) {
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$tmp = $rMin;
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$rMin = $rMax;
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$rMax = $tmp;
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}
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if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0.0)) {
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return ExcelError::NAN();
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}
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return self::calculateInverse($probability, $alpha, $beta, $rMin, $rMax);
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}
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private static function calculateInverse(float $probability, float $alpha, float $beta, float $rMin, float $rMax): string|float
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{
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$a = 0;
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$b = 2;
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$guess = ($a + $b) / 2;
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$i = 0;
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while ((($b - $a) > Functions::PRECISION) && (++$i <= self::MAX_ITERATIONS)) {
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$guess = ($a + $b) / 2;
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$result = self::distribution($guess, $alpha, $beta);
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if (($result === $probability) || ($result === 0.0)) {
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$b = $a;
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} elseif ($result > $probability) {
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$b = $guess;
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} else {
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$a = $guess;
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}
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}
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if ($i === self::MAX_ITERATIONS) {
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return ExcelError::NA();
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}
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return round($rMin + $guess * ($rMax - $rMin), 12);
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}
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/**
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* Incomplete beta function.
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*
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* @author Jaco van Kooten
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* @author Paul Meagher
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*
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* The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
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*
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* @param float $x require 0<=x<=1
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* @param float $p require p>0
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* @param float $q require q>0
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*
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* @return float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
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*/
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public static function incompleteBeta(float $x, float $p, float $q): float
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{
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if ($x <= 0.0) {
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return 0.0;
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} elseif ($x >= 1.0) {
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return 1.0;
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} elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
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return 0.0;
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}
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$beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
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if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
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return $beta_gam * self::betaFraction($x, $p, $q) / $p;
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}
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return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q);
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}
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// Function cache for logBeta function
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private static float $logBetaCacheP = 0.0;
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private static float $logBetaCacheQ = 0.0;
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private static float $logBetaCacheResult = 0.0;
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/**
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* The natural logarithm of the beta function.
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*
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* @param float $p require p>0
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* @param float $q require q>0
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*
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* @return float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
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*
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* @author Jaco van Kooten
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*/
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private static function logBeta(float $p, float $q): float
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{
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if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) {
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self::$logBetaCacheP = $p;
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self::$logBetaCacheQ = $q;
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if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
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self::$logBetaCacheResult = 0.0;
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} else {
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self::$logBetaCacheResult = Gamma::logGamma($p) + Gamma::logGamma($q) - Gamma::logGamma($p + $q);
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}
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}
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return self::$logBetaCacheResult;
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}
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/**
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* Evaluates of continued fraction part of incomplete beta function.
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* Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
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*
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* @author Jaco van Kooten
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*/
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private static function betaFraction(float $x, float $p, float $q): float
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{
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$c = 1.0;
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$sum_pq = $p + $q;
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$p_plus = $p + 1.0;
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$p_minus = $p - 1.0;
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$h = 1.0 - $sum_pq * $x / $p_plus;
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if (abs($h) < self::XMININ) {
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$h = self::XMININ;
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}
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$h = 1.0 / $h;
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$frac = $h;
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$m = 1;
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$delta = 0.0;
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while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::PRECISION) {
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$m2 = 2 * $m;
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// even index for d
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$d = $m * ($q - $m) * $x / (($p_minus + $m2) * ($p + $m2));
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$h = 1.0 + $d * $h;
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if (abs($h) < self::XMININ) {
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$h = self::XMININ;
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}
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$h = 1.0 / $h;
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$c = 1.0 + $d / $c;
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if (abs($c) < self::XMININ) {
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$c = self::XMININ;
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}
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$frac *= $h * $c;
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// odd index for d
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$d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
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$h = 1.0 + $d * $h;
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if (abs($h) < self::XMININ) {
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$h = self::XMININ;
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}
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$h = 1.0 / $h;
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$c = 1.0 + $d / $c;
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if (abs($c) < self::XMININ) {
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$c = self::XMININ;
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}
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$delta = $h * $c;
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$frac *= $delta;
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++$m;
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}
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return $frac;
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}
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/*
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private static function betaValue(float $a, float $b): float
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{
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return (Gamma::gammaValue($a) * Gamma::gammaValue($b)) /
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Gamma::gammaValue($a + $b);
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}
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private static function regularizedIncompleteBeta(float $value, float $a, float $b): float
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{
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return self::incompleteBeta($value, $a, $b) / self::betaValue($a, $b);
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}
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*/
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}
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