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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
class Beta
{
use ArrayEnabled;
private const MAX_ITERATIONS = 256;
private const LOG_GAMMA_X_MAX_VALUE = 2.55e305;
private const XMININ = 2.23e-308;
/**
* BETADIST.
*
* Returns the beta distribution.
*
* @param mixed $value Float value at which you want to evaluate the distribution
* Or can be an array of values
* @param mixed $alpha Parameter to the distribution as a float
* Or can be an array of values
* @param mixed $beta Parameter to the distribution as a float
* Or can be an array of values
* @param mixed $rMin as an float
* Or can be an array of values
* @param mixed $rMax as an float
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function distribution($value, $alpha, $beta, $rMin = 0.0, $rMax = 1.0)
{
if (is_array($value) || is_array($alpha) || is_array($beta) || is_array($rMin) || is_array($rMax)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $alpha, $beta, $rMin, $rMax);
}
$rMin = $rMin ?? 0.0;
$rMax = $rMax ?? 1.0;
try {
$value = DistributionValidations::validateFloat($value);
$alpha = DistributionValidations::validateFloat($alpha);
$beta = DistributionValidations::validateFloat($beta);
$rMax = DistributionValidations::validateFloat($rMax);
$rMin = DistributionValidations::validateFloat($rMin);
} catch (Exception $e) {
return $e->getMessage();
}
if ($rMin > $rMax) {
$tmp = $rMin;
$rMin = $rMax;
$rMax = $tmp;
}
if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
return ExcelError::NAN();
}
$value -= $rMin;
$value /= ($rMax - $rMin);
return self::incompleteBeta($value, $alpha, $beta);
}
/**
* BETAINV.
*
* Returns the inverse of the Beta distribution.
*
* @param mixed $probability Float probability at which you want to evaluate the distribution
* Or can be an array of values
* @param mixed $alpha Parameter to the distribution as a float
* Or can be an array of values
* @param mixed $beta Parameter to the distribution as a float
* Or can be an array of values
* @param mixed $rMin Minimum value as a float
* Or can be an array of values
* @param mixed $rMax Maximum value as a float
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverse($probability, $alpha, $beta, $rMin = 0.0, $rMax = 1.0)
{
if (is_array($probability) || is_array($alpha) || is_array($beta) || is_array($rMin) || is_array($rMax)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $alpha, $beta, $rMin, $rMax);
}
$rMin = $rMin ?? 0.0;
$rMax = $rMax ?? 1.0;
try {
$probability = DistributionValidations::validateProbability($probability);
$alpha = DistributionValidations::validateFloat($alpha);
$beta = DistributionValidations::validateFloat($beta);
$rMax = DistributionValidations::validateFloat($rMax);
$rMin = DistributionValidations::validateFloat($rMin);
} catch (Exception $e) {
return $e->getMessage();
}
if ($rMin > $rMax) {
$tmp = $rMin;
$rMin = $rMax;
$rMax = $tmp;
}
if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0.0)) {
return ExcelError::NAN();
}
return self::calculateInverse($probability, $alpha, $beta, $rMin, $rMax);
}
/**
* @return float|string
*/
private static function calculateInverse(float $probability, float $alpha, float $beta, float $rMin, float $rMax)
{
$a = 0;
$b = 2;
$i = 0;
while ((($b - $a) > Functions::PRECISION) && (++$i <= self::MAX_ITERATIONS)) {
$guess = ($a + $b) / 2;
$result = self::distribution($guess, $alpha, $beta);
if (($result === $probability) || ($result === 0.0)) {
$b = $a;
} elseif ($result > $probability) {
$b = $guess;
} else {
$a = $guess;
}
}
if ($i === self::MAX_ITERATIONS) {
return ExcelError::NA();
}
return round($rMin + $guess * ($rMax - $rMin), 12);
}
/**
* 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 float $x require 0<=x<=1
* @param float $p require p>0
* @param float $q require q>0
*
* @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
*/
public static function incompleteBeta(float $x, float $p, float $q): float
{
if ($x <= 0.0) {
return 0.0;
} elseif ($x >= 1.0) {
return 1.0;
} elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::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) / $p;
}
return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q);
}
// Function cache for logBeta function
private static $logBetaCacheP = 0.0;
private static $logBetaCacheQ = 0.0;
private static $logBetaCacheResult = 0.0;
/**
* The natural logarithm of the beta function.
*
* @param float $p require p>0
* @param float $q require q>0
*
* @return float 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(float $p, float $q): float
{
if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) {
self::$logBetaCacheP = $p;
self::$logBetaCacheQ = $q;
if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
self::$logBetaCacheResult = 0.0;
} else {
self::$logBetaCacheResult = Gamma::logGamma($p) + Gamma::logGamma($q) - Gamma::logGamma($p + $q);
}
}
return self::$logBetaCacheResult;
}
/**
* 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(float $x, float $p, float $q): float
{
$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) < self::XMININ) {
$h = self::XMININ;
}
$h = 1.0 / $h;
$frac = $h;
$m = 1;
$delta = 0.0;
while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::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) < self::XMININ) {
$h = self::XMININ;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (abs($c) < self::XMININ) {
$c = self::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) < self::XMININ) {
$h = self::XMININ;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (abs($c) < self::XMININ) {
$c = self::XMININ;
}
$delta = $h * $c;
$frac *= $delta;
++$m;
}
return $frac;
}
private static function betaValue(float $a, float $b): float
{
return (Gamma::gammaValue($a) * Gamma::gammaValue($b)) /
Gamma::gammaValue($a + $b);
}
private static function regularizedIncompleteBeta(float $value, float $a, float $b): float
{
return self::incompleteBeta($value, $a, $b) / self::betaValue($a, $b);
}
}
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