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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\Functions;
18use phpOMS\Math\Functions\Gamma;
19
20/**
21 * Well known functions class.
22 *
23 * @package phpOMS\Math\Stochastic\Distribution
24 * @license OMS License 2.0
25 * @link    https://jingga.app
26 * @since   1.0.0
27 */
28final class PoissonDistribution
29{
30    /**
31     * Get density.
32     *
33     * Formula: e^(k * ln(lambda) - lambda - \log(gamma(k+1))
34     *
35     * @param int   $k      Value k
36     * @param float $lambda Lambda
37     *
38     * @return float
39     *
40     * @since 1.0.0
41     */
42    public static function getPmf(int $k, float $lambda) : float
43    {
44        return \exp($k * \log($lambda) - $lambda - \log(Gamma::getGammaInteger($k + 1)));
45    }
46
47    /**
48     * Get cumulative distribution function.
49     *
50     * @param int   $k      Value k
51     * @param float $lambda Lambda
52     *
53     * @return float
54     *
55     * @since 1.0.0
56     */
57    public static function getCdf(int $k, float $lambda) : float
58    {
59        $sum = 0.0;
60
61        for ($i = 0; $i < $k + 1; ++$i) {
62            $sum += \pow($lambda, $i) / Functions::fact($i);
63        }
64
65        return \exp(-$lambda) * $sum;
66    }
67
68    /**
69     * Get mode.
70     *
71     * @param float $lambda Lambda
72     *
73     * @return float
74     *
75     * @since 1.0.0
76     */
77    public static function getMode(float $lambda) : float
78    {
79        return \floor($lambda);
80    }
81
82    /**
83     * Get expected value.
84     *
85     * @param float $lambda Lambda
86     *
87     * @return float
88     *
89     * @since 1.0.0
90     */
91    public static function getMean(float $lambda) : float
92    {
93        return $lambda;
94    }
95
96    /**
97     * Get median.
98     *
99     * @param float $lambda Lambda
100     *
101     * @return float
102     *
103     * @since 1.0.0
104     */
105    public static function getMedian(float $lambda) : float
106    {
107        return \floor($lambda + 1 / 3 - 0.02 / $lambda);
108    }
109
110    /**
111     * Get variance.
112     *
113     * @param float $lambda Lambda
114     *
115     * @return float
116     *
117     * @since 1.0.0
118     */
119    public static function getVariance(float $lambda) : float
120    {
121        return $lambda;
122    }
123
124    /**
125     * Get standard deviation.
126     *
127     * @param float $lambda Lambda
128     *
129     * @return float
130     *
131     * @since 1.0.0
132     */
133    public static function getStandardDeviation(float $lambda) : float
134    {
135        return \sqrt($lambda);
136    }
137
138    /**
139     * Get moment generating function.
140     *
141     * @param float $lambda Lambda
142     * @param float $t      Value t
143     *
144     * @return float
145     *
146     * @since 1.0.0
147     */
148    public static function getMgf(float $lambda, float $t) : float
149    {
150        return \exp($lambda * (\exp($t) - 1));
151    }
152
153    /**
154     * Get skewness.
155     *
156     * @param float $lambda Lambda
157     *
158     * @return float
159     *
160     * @since 1.0.0
161     */
162    public static function getSkewness(float $lambda) : float
163    {
164        return \pow($lambda, -1 / 2);
165    }
166
167    /**
168     * Get Fisher information.
169     *
170     * @param float $lambda Lambda
171     *
172     * @return float
173     *
174     * @since 1.0.0
175     */
176    public static function getFisherInformation(float $lambda) : float
177    {
178        return \pow($lambda, -1);
179    }
180
181    /**
182     * Get Ex. kurtosis.
183     *
184     * @param float $lambda Lambda
185     *
186     * @return float
187     *
188     * @since 1.0.0
189     */
190    public static function getExKurtosis(float $lambda) : float
191    {
192        return \pow($lambda, -1);
193    }
194}