phpOMS/Math/Stochastic/Distribution/NormalDistribution.php

<?php
/**
 * Orange Management
 *
 * PHP Version 7.2
 *
 * @package    phpOMS\Math\Stochastic\Distribution
 * @copyright  Dennis Eichhorn
 * @license    OMS License 1.0
 * @version    1.0.0
 * @link       http://website.orange-management.de
 */
declare(strict_types=1);

namespace phpOMS\Math\Stochastic\Distribution;

/**
 * Normal distribution.
 *
 * @package    phpOMS\Math\Stochastic\Distribution
 * @license    OMS License 1.0
 * @link       http://website.orange-management.de
 * @since      1.0.0
 */
class NormalDistribution
{

    /**
     * Get probability density function.
     *
     * @param float $x   Value x
     * @param float $mu  Value mu
     * @param float $sig Sigma
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getPdf(float $x, float $mu, float $sig) : float
    {
        return 1 / ($sig * \sqrt(2 * pi())) * \exp(-($x - $mu) ** 2 / (2 * $sig ** 2));
    }

    /**
     * Get probability density function.
     *
     * @param float $x   Value x
     * @param float $mu  Value mu
     * @param float $sig Sigma
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getCdf(float $x, float $mu, float $sig) : float
    {
        return 1 / 2 * (1 + self::erf(($x - $mu) / ($sig * \sqrt(2))));
    }

    /**
     * Error function approximation
     *
     * @param float $x Value x
     *
     * @return float
     *
     * @since  1.0.0
     */
    private static function erf(float $x) : float
    {
        if ($x < 0) {
            return -self::erf(-$x);
        }

        $a = 8 * (pi() - 3) / (3 * pi() * (4 - pi()));

        return \sqrt(1 - \exp(-($x ** 2) * (4 / pi() + $a * $x ** 2) / (1 + $a * $x ** 2)));
    }

    /**
     * Get mode.
     *
     * @param float $mu Value mu
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getMode(float $mu) : float
    {
        return $mu;
    }

    /**
     * Get expected value.
     *
     * @param float $mu Value mu
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getMean(float $mu) : float
    {
        return $mu;
    }

    /**
     * Get expected value.
     *
     * @param float $mu Value mu
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getMedian(float $mu) : float
    {
        return $mu;
    }

    /**
     * Get variance.
     *
     * @param float $sig Sigma
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getVariance(float $sig) : float
    {
        return $sig ** 2;
    }

    /**
     * Get moment generating function.
     *
     * @param float $t   Value t
     * @param float $mu  Value mu
     * @param float $sig Sigma
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getMgf(float $t, float $mu, float $sig) : float
    {
        return \exp($mu * $t + ($sig ** 2 * $t ** 2) / 2);
    }

    /**
     * Get skewness.
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getSkewness() : float
    {
        return 0;
    }

    /**
     * Get Fisher information.
     *
     * @param float $sig Sigma
     *
     * @return array
     *
     * @since  1.0.0
     */
    public static function getFisherInformation(float $sig) : array
    {
        return [[1 / $sig ** 2, 0], [0, 1 / (2 * $sig ** 4)]];
    }

    /**
     * Get Ex. kurtosis.
     *
     * @return float
     *
     * @since  1.0.0
     */
    public static function getExKurtosis() : float
    {
        return 0;
    }
}