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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
17use phpOMS\Math\Functions\Beta;
18
19/**
20 * Log distribution.
21 *
22 * @package phpOMS\Math\Stochastic\Distribution
23 * @license OMS License 2.0
24 * @link    https://jingga.app
25 * @since   1.0.0
26 */
27final class LogDistribution
28{
29    /**
30     * Epsilon for float comparison.
31     *
32     * @var float
33     * @since 1.0.0
34     */
35    public const EPSILON = 4.88e-04;
36
37    /**
38     * Get probability mass function.
39     *
40     * @latex -\frac{1}{\log(1-p)} \cdot \frac{p^k}{k}
41     *
42     * @param float $p Value p
43     * @param int   $k Value k
44     *
45     * @return float
46     *
47     * @since 1.0.0
48     */
49    public static function getPmf(float $p, int $k) : float
50    {
51        return -1 / \log(1 - $p) * $p ** $k / $k;
52    }
53
54    /**
55     * Get cumulative distribution function.
56     *
57     * @param float $p Value p
58     * @param int   $k Value k
59     *
60     * @return float
61     *
62     * @since 1.0.0
63     */
64    public static function getCdf(float $p, int $k) : float
65    {
66        // This is a workaround!
67        // Actually 0 should be used instead of self::EPSILON.
68        // This is only used because the incomplete beta function doesn't work for p or q = 0
69        return 1 + Beta::incompleteBeta($p, $k + 1, self::EPSILON) / \log(1 - $p);
70    }
71
72    /**
73     * Get expected value.
74     *
75     * @latex -\frac{1}{\log(1-p)} \cdot \frac{p}{1-p}
76     *
77     * @param float $p Value p
78     *
79     * @return float
80     *
81     * @since 1.0.0
82     */
83    public static function getMean(float $p) : float
84    {
85        return -1 / \log(1 - $p) * $p / (1 - $p);
86    }
87
88    /**
89     * Get mode.
90     *
91     * @return int
92     *
93     * @since 1.0.0
94     */
95    public static function getMode() : int
96    {
97        return 1;
98    }
99
100    /**
101     * Get variance.
102     *
103     * @latex -\frac{p^2 + p\log(1-p)}{(1-p)^2\log(1-p)^2}
104     *
105     * @param float $p Value p
106     *
107     * @return float
108     *
109     * @since 1.0.0
110     */
111    public static function getVariance(float $p) : float
112    {
113        return -($p ** 2 + $p * \log(1 - $p))
114            / ((1 - $p) ** 2 * \log(1 - $p) ** 2);
115    }
116
117    /**
118     * Get standard deviation.
119     *
120     * @latex \sqrt{-\frac{p^2 + p\log(1-p)}{(1-p)^2\log(1-p)^2}}
121     *
122     * @param float $p Value p
123     *
124     * @return float
125     *
126     * @since 1.0.0
127     */
128    public static function getStandardDeviation(float $p) : float
129    {
130        return \sqrt(self::getVariance($p));
131    }
132
133    /**
134     * Get moment generating function.
135     *
136     * @latex \frac{\log(1-p\exp(t))}{\log(1-p)}
137     *
138     * @param float $p Value p
139     * @param float $t Value t
140     *
141     * @return float
142     *
143     * @since 1.0.0
144     */
145    public static function getMgf(float $p, float $t) : float
146    {
147        return \log(1 - $p * \exp($t)) / \log(1 - $p);
148    }
149}