mirror of
https://github.com/Karaka-Management/phpOMS.git
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275 lines
12 KiB
PHP
275 lines
12 KiB
PHP
<?php
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/**
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* Orange Management
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*
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* PHP Version 7.2
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*
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* @package phpOMS\Math\Stochastic\Distribution
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* @copyright Dennis Eichhorn
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* @license OMS License 1.0
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* @version 1.0.0
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* @link http://website.orange-management.de
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*/
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declare(strict_types=1);
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namespace phpOMS\Math\Stochastic\Distribution;
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use phpOMS\Math\Functions\Functions;
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use phpOMS\Math\Functions\Gamma;
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/**
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* Chi squared distribution.
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*
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* @package phpOMS\Math\Stochastic\Distribution
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* @license OMS License 1.0
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* @link http://website.orange-management.de
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* @since 1.0.0
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*/
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class ChiSquaredDistribution
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{
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/**
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* Chi square table.
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*
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* @var array<int, array<string, float>>
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* @since 1.0.0
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*/
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public const TABLE = [
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1 => ['0.995' => 0.000, '0.99' => 0.000, '0.975' => 0.001, '0.95' => 0.004, '0.90' => 0.016, '0.10' => 2.706, '0.05' => 3.841, '0.025' => 5.024, '0.01' => 6.635, '0.005' => 7.879],
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2 => ['0.995' => 0.010, '0.99' => 0.020, '0.975' => 0.051, '0.95' => 0.103, '0.90' => 0.211, '0.10' => 4.605, '0.05' => 5.991, '0.025' => 7.378, '0.01' => 9.210, '0.005' => 10.597],
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3 => ['0.995' => 0.072, '0.99' => 0.115, '0.975' => 0.216, '0.95' => 0.352, '0.90' => 0.584, '0.10' => 6.251, '0.05' => 7.815, '0.025' => 9.348, '0.01' => 11.345, '0.005' => 12.838],
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4 => ['0.995' => 0.207, '0.99' => 0.297, '0.975' => 0.484, '0.95' => 0.711, '0.90' => 1.064, '0.10' => 7.779, '0.05' => 9.488, '0.025' => 11.143, '0.01' => 13.277, '0.005' => 14.860],
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5 => ['0.995' => 0.412, '0.99' => 0.554, '0.975' => 0.831, '0.95' => 1.145, '0.90' => 1.610, '0.10' => 9.236, '0.05' => 11.070, '0.025' => 12.833, '0.01' => 15.086, '0.005' => 16.750],
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6 => ['0.995' => 0.676, '0.99' => 0.872, '0.975' => 1.237, '0.95' => 1.635, '0.90' => 2.204, '0.10' => 10.645, '0.05' => 12.592, '0.025' => 14.449, '0.01' => 16.812, '0.005' => 18.548],
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7 => ['0.995' => 0.989, '0.99' => 1.239, '0.975' => 1.690, '0.95' => 2.167, '0.90' => 2.833, '0.10' => 12.017, '0.05' => 14.067, '0.025' => 16.013, '0.01' => 18.475, '0.005' => 20.278],
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8 => ['0.995' => 1.344, '0.99' => 1.646, '0.975' => 2.180, '0.95' => 2.733, '0.90' => 3.490, '0.10' => 13.362, '0.05' => 15.507, '0.025' => 17.535, '0.01' => 20.090, '0.005' => 21.955],
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9 => ['0.995' => 1.735, '0.99' => 2.088, '0.975' => 2.700, '0.95' => 3.325, '0.90' => 4.168, '0.10' => 14.684, '0.05' => 16.919, '0.025' => 19.023, '0.01' => 21.666, '0.005' => 23.589],
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10 => ['0.995' => 2.156, '0.99' => 2.558, '0.975' => 3.247, '0.95' => 3.940, '0.90' => 4.865, '0.10' => 15.987, '0.05' => 18.307, '0.025' => 20.483, '0.01' => 23.209, '0.005' => 25.188],
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11 => ['0.995' => 2.603, '0.99' => 3.053, '0.975' => 3.816, '0.95' => 4.575, '0.90' => 5.578, '0.10' => 17.275, '0.05' => 19.675, '0.025' => 21.920, '0.01' => 24.725, '0.005' => 26.757],
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12 => ['0.995' => 3.074, '0.99' => 3.571, '0.975' => 4.404, '0.95' => 5.226, '0.90' => 6.304, '0.10' => 18.549, '0.05' => 21.026, '0.025' => 23.337, '0.01' => 26.217, '0.005' => 28.300],
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13 => ['0.995' => 3.565, '0.99' => 4.107, '0.975' => 5.009, '0.95' => 5.892, '0.90' => 7.042, '0.10' => 19.812, '0.05' => 22.362, '0.025' => 24.736, '0.01' => 27.688, '0.005' => 29.819],
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14 => ['0.995' => 4.075, '0.99' => 4.660, '0.975' => 5.629, '0.95' => 6.571, '0.90' => 7.790, '0.10' => 21.064, '0.05' => 23.685, '0.025' => 26.119, '0.01' => 29.141, '0.005' => 31.319],
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15 => ['0.995' => 4.601, '0.99' => 5.229, '0.975' => 6.262, '0.95' => 7.261, '0.90' => 8.547, '0.10' => 22.307, '0.05' => 24.996, '0.025' => 27.488, '0.01' => 30.578, '0.005' => 32.801],
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16 => ['0.995' => 5.142, '0.99' => 5.812, '0.975' => 6.908, '0.95' => 7.962, '0.90' => 9.312, '0.10' => 23.542, '0.05' => 26.296, '0.025' => 28.845, '0.01' => 32.000, '0.005' => 34.267],
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17 => ['0.995' => 5.697, '0.99' => 6.408, '0.975' => 7.564, '0.95' => 8.672, '0.90' => 10.085, '0.10' => 24.769, '0.05' => 27.587, '0.025' => 30.191, '0.01' => 33.409, '0.005' => 35.718],
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18 => ['0.995' => 6.265, '0.99' => 7.015, '0.975' => 8.231, '0.95' => 9.390, '0.90' => 10.865, '0.10' => 25.989, '0.05' => 28.869, '0.025' => 31.526, '0.01' => 34.805, '0.005' => 37.156],
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19 => ['0.995' => 6.844, '0.99' => 7.633, '0.975' => 8.907, '0.95' => 10.117, '0.90' => 11.651, '0.10' => 27.204, '0.05' => 30.144, '0.025' => 32.852, '0.01' => 36.191, '0.005' => 38.582],
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20 => ['0.995' => 7.434, '0.99' => 8.260, '0.975' => 9.591, '0.95' => 10.851, '0.90' => 12.443, '0.10' => 28.412, '0.05' => 31.410, '0.025' => 34.170, '0.01' => 37.566, '0.005' => 39.997],
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21 => ['0.995' => 8.034, '0.99' => 8.897, '0.975' => 10.283, '0.95' => 11.591, '0.90' => 13.240, '0.10' => 29.615, '0.05' => 32.671, '0.025' => 35.479, '0.01' => 38.932, '0.005' => 41.401],
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22 => ['0.995' => 8.643, '0.99' => 9.542, '0.975' => 10.982, '0.95' => 12.338, '0.90' => 14.041, '0.10' => 30.813, '0.05' => 33.924, '0.025' => 36.781, '0.01' => 40.289, '0.005' => 42.796],
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23 => ['0.995' => 9.260, '0.99' => 10.196, '0.975' => 11.689, '0.95' => 13.091, '0.90' => 14.848, '0.10' => 32.007, '0.05' => 35.172, '0.025' => 38.076, '0.01' => 41.638, '0.005' => 44.181],
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24 => ['0.995' => 9.886, '0.99' => 10.856, '0.975' => 12.401, '0.95' => 13.848, '0.90' => 15.659, '0.10' => 33.196, '0.05' => 36.415, '0.025' => 39.364, '0.01' => 42.980, '0.005' => 45.559],
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25 => ['0.995' => 10.520, '0.99' => 11.524, '0.975' => 13.120, '0.95' => 14.611, '0.90' => 16.473, '0.10' => 34.382, '0.05' => 37.652, '0.025' => 40.646, '0.01' => 44.314, '0.005' => 46.928],
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26 => ['0.995' => 11.160, '0.99' => 12.198, '0.975' => 13.844, '0.95' => 15.379, '0.90' => 17.292, '0.10' => 35.563, '0.05' => 38.885, '0.025' => 41.923, '0.01' => 45.642, '0.005' => 48.290],
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27 => ['0.995' => 11.808, '0.99' => 12.879, '0.975' => 14.573, '0.95' => 16.151, '0.90' => 18.114, '0.10' => 36.741, '0.05' => 40.113, '0.025' => 43.195, '0.01' => 46.963, '0.005' => 49.645],
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28 => ['0.995' => 12.461, '0.99' => 13.565, '0.975' => 15.308, '0.95' => 16.928, '0.90' => 18.939, '0.10' => 37.916, '0.05' => 41.337, '0.025' => 44.461, '0.01' => 48.278, '0.005' => 50.993],
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29 => ['0.995' => 13.121, '0.99' => 14.256, '0.975' => 16.047, '0.95' => 17.708, '0.90' => 19.768, '0.10' => 39.087, '0.05' => 42.557, '0.025' => 45.722, '0.01' => 49.588, '0.005' => 52.336],
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30 => ['0.995' => 13.787, '0.99' => 14.953, '0.975' => 16.791, '0.95' => 18.493, '0.90' => 20.599, '0.10' => 40.256, '0.05' => 43.773, '0.025' => 46.979, '0.01' => 50.892, '0.005' => 53.672],
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40 => ['0.995' => 20.707, '0.99' => 22.164, '0.975' => 24.433, '0.95' => 26.509, '0.90' => 29.051, '0.10' => 51.805, '0.05' => 55.758, '0.025' => 59.342, '0.01' => 63.691, '0.005' => 66.766],
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50 => ['0.995' => 27.991, '0.99' => 29.707, '0.975' => 32.357, '0.95' => 34.764, '0.90' => 37.689, '0.10' => 63.167, '0.05' => 67.505, '0.025' => 71.420, '0.01' => 76.154, '0.005' => 79.490],
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60 => ['0.995' => 35.534, '0.99' => 37.485, '0.975' => 40.482, '0.95' => 43.188, '0.90' => 46.459, '0.10' => 74.397, '0.05' => 79.082, '0.025' => 83.298, '0.01' => 88.379, '0.005' => 91.952],
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70 => ['0.995' => 43.275, '0.99' => 45.442, '0.975' => 48.758, '0.95' => 51.739, '0.90' => 55.329, '0.10' => 85.527, '0.05' => 90.531, '0.025' => 95.023, '0.01' => 100.425, '0.005' => 104.215],
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80 => ['0.995' => 51.172, '0.99' => 53.540, '0.975' => 57.153, '0.95' => 60.391, '0.90' => 64.278, '0.10' => 96.578, '0.05' => 101.879, '0.025' => 106.629, '0.01' => 112.329, '0.005' => 116.321],
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90 => ['0.995' => 59.196, '0.99' => 61.754, '0.975' => 65.647, '0.95' => 69.126, '0.90' => 73.291, '0.10' => 107.565, '0.05' => 113.145, '0.025' => 118.136, '0.01' => 124.116, '0.005' => 128.299],
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100 => ['0.995' => 67.328, '0.99' => 70.065, '0.975' => 74.222, '0.95' => 77.929, '0.90' => 82.358, '0.10' => 118.498, '0.05' => 124.342, '0.025' => 129.561, '0.01' => 135.807, '0.005' => 140.169],
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];
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/**
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* Test hypthesis.
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*
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* @param array $dataset Values
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* @param array $expected Expected values based on probability
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* @param float $significance Significance
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* @param int $df Degrees of freedom (optional)
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*
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* @return array
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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public static function testHypothesis(array $dataset, array $expected, float $significance = 0.05, int $df = 0) : array
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{
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if (($count = \count($dataset)) !== \count($expected)) {
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throw new \Exception('Dimension');
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}
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$sum = 0.0;
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for ($i = 0; $i < $count; ++$i) {
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$sum += ($dataset[$i] - $expected[$i]) * ($dataset[$i] - $expected[$i]) / $expected[$i];
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}
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$p = null;
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if ($df === 0) {
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$df = self::getDegreesOfFreedom($dataset);
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}
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if (!defined('self::TABLE') || !array_key_exists($df, self::TABLE)) {
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throw new \Exception('Degrees of freedom not supported');
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}
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foreach (self::TABLE[$df] as $key => $value) {
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if ($value > $sum) {
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$p = $key;
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break;
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}
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}
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$key = \key(\end(self::TABLE[$df]));
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$p = 1 - ($p ?? ($key === false ? 1 : (float) $key));
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return ['P' => $p, 'H0' => ($p > $significance), 'df' => $df];
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}
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/**
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* Get degrees of freedom of array.
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*
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* @param array $values Value matrix or vector (N or NxM)
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public static function getDegreesOfFreedom(array $values) : int
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{
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if (is_array($first = \reset($values))) {
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return (\count($values) - 1) * (\count($first) - 1);
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} else {
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return \count($values) - 1;
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}
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}
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/**
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* Get probability density function.
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*
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* @param float $x Value x
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* @param int $df Degreegs of freedom
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*
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* @return float
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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public static function getPdf(float $x, int $df) : float
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{
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if ($x < 0) {
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throw new \Exception('Out of bounds');
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}
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return 1 / (\pow(2, $df / 2) * Gamma::lanczosApproximationReal(($df / 2))) * \pow($x, $df / 2 - 1) * \exp(-$x / 2);
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}
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/**
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* Get mode.
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*
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* @param int $df Degrees of freedom
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public static function getMode(int $df) : int
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{
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return \max([$df - 2, 0]);
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}
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/**
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* Get expected value.
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*
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* @param int $df Degrees of freedom
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function getMean(int $df) : float
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{
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return $df;
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}
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/**
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* Get expected value.
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*
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* @param int $df Degrees of freedom
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function getMedian(int $df) : float
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{
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return $df * (1 - 2 / (9 * $df)) ** 3;
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}
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/**
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* Get variance.
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*
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* @param int $df Degrees of freedom
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function getVariance(int $df) : float
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{
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return 2 * $df;
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}
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/**
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* Get moment generating function.
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*
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* @param int $df Degrees of freedom
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* @param float $t Value t
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*
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* @return float
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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public static function getMgf(int $df, float $t) : float
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{
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if ($t > 0.5) {
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throw new \Exception('Out of bounds');
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}
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return \pow(1 - 2 * $t, -$df / 2);
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}
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/**
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* Get skewness.
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*
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* @param int $df Degrees of freedom
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function getSkewness(int $df) : float
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{
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return \sqrt(8 / $df);
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}
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/**
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* Get Ex. kurtosis.
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*
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* @param int $df Degrees of freedom
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function getExKurtosis(int $df) : float
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{
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return 12 / $df;
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}
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public static function getRandom()
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{
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}
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}
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