phpOMS/Math/Stochastic/Distribution/WeibullDistribution.php

<?php
/**
 * Karaka
 *
 * PHP Version 8.1
 *
 * @package   phpOMS\Math\Stochastic\Distribution
 * @copyright Dennis Eichhorn
 * @license   OMS License 1.0
 * @version   1.0.0
 * @link      https://karaka.app
 */
declare(strict_types=1);

namespace phpOMS\Math\Stochastic\Distribution;

use phpOMS\Math\Functions\Gamma;

/**
 * Weibull distribution.
 *
 * @package phpOMS\Math\Stochastic\Distribution
 * @license OMS License 1.0
 * @link    https://karaka.app
 * @since   1.0.0
 */
final class WeibullDistribution
{
    /**
     * Get probability density function.
     *
     * @param float $x      Value x
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getPdf(float $x, float $lambda, float $k) : float
    {
        return $x < 0.0
            ? 0.0
            : $k / $lambda * \pow($x / $lambda, $k - 1) * \exp(-($x / $lambda) ** $k);
    }

    /**
     * Get cumulative distribution function.
     *
     * @param float $x      Value x
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getCdf(float $x, float $lambda, float $k) : float
    {
        return $x < 0.0
            ? 0.0
            : 1 - \exp(-($x / $lambda) ** $k);
    }

    /**
     * Get mean.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMean(float $lambda, float $k) : float
    {
        return $lambda * Gamma::gamma(1 + 1 / $k);
    }

    /**
     * Get median.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMedian(float $lambda, float $k) : float
    {
        return $lambda * \pow(\log(2), 1 / $k);
    }

    /**
     * Get the variance.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getVariance(float $lambda, float $k) : float
    {
        return $lambda ** 2 * (Gamma::gamma(1 + 2 / $k) - Gamma::gamma(1 + 1 / $k) ** 2);
    }

    /**
     * Get the standard deviation.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getStandardDeviation(float $lambda, float $k) : float
    {
        return \sqrt(self::getVariance($lambda, $k));
    }

    /**
     * Get mode.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMode(float $lambda, float $k) : float
    {
        return $lambda * \pow(($k - 1) / $k, 1 / $k);
    }

    /**
     * Get skewness.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getSkewness(float $lambda, float $k) : float
    {
        $mu  = self::getMean($lambda, $k);
        $sig = self::getStandardDeviation($lambda, $k);

        return (Gamma::gamma(1 + 3 / $k) * $lambda ** 3 - 3 * $mu * $sig ** 2 - $mu ** 3)
            / ($sig ** 3);
    }

    /**
     * Get entropy.
     *
     * @param float $lambda Scale lambda
     * @param float $k      Shape k
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getEntropy(float $lambda, float $k) : float
    {
        $gamma = 0.57721566490153286060651209008240243104215933593992;

        return $gamma * (1 - 1 / $k) + \log($lambda / $k) + 1;
    }
}