phpOMS/Math/Stochastic/Distribution/UniformDistributionContinuous.php

<?php
/**
 * Orange Management
 *
 * PHP Version 7.4
 *
 * @package   phpOMS\Math\Stochastic\Distribution
 * @copyright Dennis Eichhorn
 * @license   OMS License 1.0
 * @version   1.0.0
 * @link      https://orange-management.org
 */
declare(strict_types=1);

namespace phpOMS\Math\Stochastic\Distribution;

/**
 * Uniform (continuous) distribution.
 *
 * @package phpOMS\Math\Stochastic\Distribution
 * @license OMS License 1.0
 * @link    https://orange-management.org
 * @since   1.0.0
 */
class UniformDistributionContinuous
{

    /**
     * Get mode.
     *
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMode(float $a, float $b) : float
    {
        return ($a + $b) / 2;
    }

    /**
     * Get probability density function.
     *
     * @param float $x Value x
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getPdf(float $x, float $a, float $b) : float
    {
        return $x > $a && $x < $b ? 1 / ($b - $a) : 0;
    }

    /**
     * Get cumulative distribution function.
     *
     * @param float $x Value x
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getCdf(float $x, float $a, float $b) : float
    {
        if ($x < $a) {
            return 0;
        } elseif ($x >= $a && $x < $b) {
            return ($x - $a) / ($b - $a);
        } else {
            return 1;
        }
    }

    /**
     * Get moment generating function.
     *
     * @param int   $t Value t
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMgf(int $t, float $a, float $b) : float
    {
        return $t === 0 ? 1 : (\exp($t * $b) - \exp($t * $a)) / ($t * ($b - $a));
    }

    /**
     * Get skewness.
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getSkewness() : float
    {
        return 0.0;
    }

    /**
     * Get Ex. kurtosis.
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getExKurtosis() : float
    {
        return -6 / 5;
    }

    /**
     * Get median.
     *
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMedian(float $a, float $b) : float
    {
        return ($a + $b) / 2;
    }

    /**
     * Get expected value.
     *
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getMean(float $a, float $b) : float
    {
        return ($a + $b) / 2;
    }

    /**
     * Get variance.
     *
     * @param float $a Value a
     * @param float $b Value b
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function getVariance(float $a, float $b) : float
    {
        return 1 / 12 * ($b - $a) ** 2;
    }
}