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1<?php
2/**
3 * Jingga
4 *
5 * PHP Version 8.1
6 *
7 * @package   phpOMS\Math\Stochastic\Distribution
8 * @copyright Dennis Eichhorn
9 * @license   OMS License 2.0
10 * @version   1.0.0
11 * @link      https://jingga.app
12 */
13declare(strict_types=1);
14
15namespace phpOMS\Math\Stochastic\Distribution;
16
17/**
18 * Laplace distribution.
19 *
20 * @package phpOMS\Math\Stochastic\Distribution
21 * @license OMS License 2.0
22 * @link    https://jingga.app
23 * @since   1.0.0
24 */
25final class LaplaceDistribution
26{
27    /**
28     * Get probability density function.
29     *
30     * @param float $x  Value x
31     * @param float $mu Mean
32     * @param float $b  Value b
33     *
34     * @return float
35     *
36     * @since 1.0.0
37     */
38    public static function getPdf(float $x, float $mu, float $b) : float
39    {
40        return 1 / (2 * $b) * \exp(-\abs($x - $mu) / $b);
41    }
42
43    /**
44     * Get cumulative distribution function.
45     *
46     * @param float $x  Value x
47     * @param float $mu Mean
48     * @param float $b  Value b
49     *
50     * @return float
51     *
52     * @since 1.0.0
53     */
54    public static function getCdf(float $x, float $mu, float $b) : float
55    {
56        return $x < $mu ? \exp(($x - $mu) / $b) / 2 : 1 - \exp(-($x - $mu) / $b) / 2;
57    }
58
59    /**
60     * Get mode.
61     *
62     * @param float $mu Mean
63     *
64     * @return float
65     *
66     * @since 1.0.0
67     */
68    public static function getMode(float $mu) : float
69    {
70        return $mu;
71    }
72
73    /**
74     * Get expected value.
75     *
76     * @param float $mu Mean
77     *
78     * @return float
79     *
80     * @since 1.0.0
81     */
82    public static function getMean(float $mu) : float
83    {
84        return $mu;
85    }
86
87    /**
88     * Get median.
89     *
90     * @param float $mu Mean
91     *
92     * @return float
93     *
94     * @since 1.0.0
95     */
96    public static function getMedian(float $mu) : float
97    {
98        return $mu;
99    }
100
101    /**
102     * Get variance.
103     *
104     * @param float $b Value b
105     *
106     * @return float
107     *
108     * @since 1.0.0
109     */
110    public static function getVariance(float $b) : float
111    {
112        return 2 * $b ** 2;
113    }
114
115    /**
116     * Get standard deviation.
117     *
118     * @param float $b Value b
119     *
120     * @return float
121     *
122     * @since 1.0.0
123     */
124    public static function getStandardDeviation(float $b) : float
125    {
126        return \sqrt(self::getVariance($b));
127    }
128
129    /**
130     * Get moment generating function.
131     *
132     * @param float $t  Valute t
133     * @param float $mu Mean
134     * @param float $b  Value b
135     *
136     * @return float
137     *
138     * @throws \OutOfBoundsException
139     *
140     * @since 1.0.0
141     */
142    public static function getMgf(float $t, float $mu, float $b) : float
143    {
144        if (\abs($t) >= 1 / $b) {
145            throw new \OutOfBoundsException('Out of bounds');
146        }
147
148        return \exp($mu * $t) / (1 - $b ** 2 * $t ** 2);
149    }
150
151    /**
152     * Get skewness.
153     *
154     * @return float
155     *
156     * @since 1.0.0
157     */
158    public static function getSkewness() : float
159    {
160        return 0;
161    }
162
163    /**
164     * Get Ex. kurtosis.
165     *
166     * @return float
167     *
168     * @since 1.0.0
169     */
170    public static function getExKurtosis() : float
171    {
172        return 3;
173    }
174}