mirror of
https://github.com/Karaka-Management/phpOMS.git
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163 lines
8.9 KiB
PHP
163 lines
8.9 KiB
PHP
<?php
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/**
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* Orange Management
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*
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* PHP Version 7.4
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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 https://orange-management.org
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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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/**
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* Bernulli 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 https://orange-management.org
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* @since 1.0.0
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*/
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final class TDistribution
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{
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/**
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* T table.
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*
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* [degrees of freedom = df]
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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' => 0.000, '0.5' => 1.000, '0.6' => 1.376, '0.7' => 1.963, '0.8' => 3.078, '0.9' => 6.314, '0.95' => 12.71, '0.98' => 31.82, '0.99' => 63.66, '0.998' => 318.31, '0.999' => 636.62,],
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2 => ['0' => 0.000, '0.5' => 0.816, '0.6' => 1.061, '0.7' => 1.386, '0.8' => 1.886, '0.9' => 2.920, '0.95' => 4.303, '0.98' => 6.965, '0.99' => 9.925, '0.998' => 22.327, '0.999' => 31.599,],
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3 => ['0' => 0.000, '0.5' => 0.765, '0.6' => 0.978, '0.7' => 1.250, '0.8' => 1.638, '0.9' => 2.353, '0.95' => 3.182, '0.98' => 4.541, '0.99' => 5.841, '0.998' => 10.215, '0.999' => 12.924,],
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4 => ['0' => 0.000, '0.5' => 0.741, '0.6' => 0.941, '0.7' => 1.190, '0.8' => 1.533, '0.9' => 2.132, '0.95' => 2.776, '0.98' => 3.747, '0.99' => 4.604, '0.998' => 7.173, '0.999' => 8.610,],
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5 => ['0' => 0.000, '0.5' => 0.727, '0.6' => 0.920, '0.7' => 1.156, '0.8' => 1.476, '0.9' => 2.015, '0.95' => 2.571, '0.98' => 3.365, '0.99' => 4.032, '0.998' => 5.893, '0.999' => 6.869,],
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6 => ['0' => 0.000, '0.5' => 0.718, '0.6' => 0.906, '0.7' => 1.134, '0.8' => 1.440, '0.9' => 1.943, '0.95' => 2.447, '0.98' => 3.143, '0.99' => 3.707, '0.998' => 5.208, '0.999' => 5.959,],
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7 => ['0' => 0.000, '0.5' => 0.711, '0.6' => 0.896, '0.7' => 1.119, '0.8' => 1.415, '0.9' => 1.895, '0.95' => 2.365, '0.98' => 2.998, '0.99' => 3.499, '0.998' => 4.785, '0.999' => 5.408,],
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8 => ['0' => 0.000, '0.5' => 0.706, '0.6' => 0.889, '0.7' => 1.108, '0.8' => 1.397, '0.9' => 1.860, '0.95' => 2.306, '0.98' => 2.896, '0.99' => 3.355, '0.998' => 4.501, '0.999' => 5.041,],
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9 => ['0' => 0.000, '0.5' => 0.703, '0.6' => 0.883, '0.7' => 1.100, '0.8' => 1.383, '0.9' => 1.833, '0.95' => 2.262, '0.98' => 2.821, '0.99' => 3.250, '0.998' => 4.297, '0.999' => 4.781,],
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10 => ['0' => 0.000, '0.5' => 0.700, '0.6' => 0.879, '0.7' => 1.093, '0.8' => 1.372, '0.9' => 1.812, '0.95' => 2.228, '0.98' => 2.764, '0.99' => 3.169, '0.998' => 4.144, '0.999' => 4.587,],
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11 => ['0' => 0.000, '0.5' => 0.697, '0.6' => 0.876, '0.7' => 1.088, '0.8' => 1.363, '0.9' => 1.796, '0.95' => 2.201, '0.98' => 2.718, '0.99' => 3.106, '0.998' => 4.025, '0.999' => 4.437,],
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12 => ['0' => 0.000, '0.5' => 0.695, '0.6' => 0.873, '0.7' => 1.083, '0.8' => 1.356, '0.9' => 1.782, '0.95' => 2.179, '0.98' => 2.681, '0.99' => 3.055, '0.998' => 3.930, '0.999' => 4.318,],
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13 => ['0' => 0.000, '0.5' => 0.694, '0.6' => 0.870, '0.7' => 1.079, '0.8' => 1.350, '0.9' => 1.771, '0.95' => 2.160, '0.98' => 2.650, '0.99' => 3.012, '0.998' => 3.852, '0.999' => 4.221,],
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14 => ['0' => 0.000, '0.5' => 0.692, '0.6' => 0.868, '0.7' => 1.076, '0.8' => 1.345, '0.9' => 1.761, '0.95' => 2.145, '0.98' => 2.624, '0.99' => 2.977, '0.998' => 3.787, '0.999' => 4.140,],
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15 => ['0' => 0.000, '0.5' => 0.691, '0.6' => 0.866, '0.7' => 1.074, '0.8' => 1.341, '0.9' => 1.753, '0.95' => 2.131, '0.98' => 2.602, '0.99' => 2.947, '0.998' => 3.733, '0.999' => 4.073,],
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16 => ['0' => 0.000, '0.5' => 0.690, '0.6' => 0.865, '0.7' => 1.071, '0.8' => 1.337, '0.9' => 1.746, '0.95' => 2.120, '0.98' => 2.583, '0.99' => 2.921, '0.998' => 3.686, '0.999' => 4.015,],
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17 => ['0' => 0.000, '0.5' => 0.689, '0.6' => 0.863, '0.7' => 1.069, '0.8' => 1.333, '0.9' => 1.740, '0.95' => 2.110, '0.98' => 2.567, '0.99' => 2.898, '0.998' => 3.646, '0.999' => 3.965,],
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18 => ['0' => 0.000, '0.5' => 0.688, '0.6' => 0.862, '0.7' => 1.067, '0.8' => 1.330, '0.9' => 1.734, '0.95' => 2.101, '0.98' => 2.552, '0.99' => 2.878, '0.998' => 3.610, '0.999' => 3.922,],
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19 => ['0' => 0.000, '0.5' => 0.688, '0.6' => 0.861, '0.7' => 1.066, '0.8' => 1.328, '0.9' => 1.729, '0.95' => 2.093, '0.98' => 2.539, '0.99' => 2.861, '0.998' => 3.579, '0.999' => 3.883,],
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20 => ['0' => 0.000, '0.5' => 0.687, '0.6' => 0.860, '0.7' => 1.064, '0.8' => 1.325, '0.9' => 1.725, '0.95' => 2.086, '0.98' => 2.528, '0.99' => 2.845, '0.998' => 3.552, '0.999' => 3.850,],
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21 => ['0' => 0.000, '0.5' => 0.686, '0.6' => 0.859, '0.7' => 1.063, '0.8' => 1.323, '0.9' => 1.721, '0.95' => 2.080, '0.98' => 2.518, '0.99' => 2.831, '0.998' => 3.527, '0.999' => 3.819,],
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22 => ['0' => 0.000, '0.5' => 0.686, '0.6' => 0.858, '0.7' => 1.061, '0.8' => 1.321, '0.9' => 1.717, '0.95' => 2.074, '0.98' => 2.508, '0.99' => 2.819, '0.998' => 3.505, '0.999' => 3.792,],
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23 => ['0' => 0.000, '0.5' => 0.685, '0.6' => 0.858, '0.7' => 1.060, '0.8' => 1.319, '0.9' => 1.714, '0.95' => 2.069, '0.98' => 2.500, '0.99' => 2.807, '0.998' => 3.485, '0.999' => 3.768,],
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24 => ['0' => 0.000, '0.5' => 0.685, '0.6' => 0.857, '0.7' => 1.059, '0.8' => 1.318, '0.9' => 1.711, '0.95' => 2.064, '0.98' => 2.492, '0.99' => 2.797, '0.998' => 3.467, '0.999' => 3.745,],
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25 => ['0' => 0.000, '0.5' => 0.684, '0.6' => 0.856, '0.7' => 1.058, '0.8' => 1.316, '0.9' => 1.708, '0.95' => 2.060, '0.98' => 2.485, '0.99' => 2.787, '0.998' => 3.450, '0.999' => 3.725,],
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26 => ['0' => 0.000, '0.5' => 0.684, '0.6' => 0.856, '0.7' => 1.058, '0.8' => 1.315, '0.9' => 1.706, '0.95' => 2.056, '0.98' => 2.479, '0.99' => 2.779, '0.998' => 3.435, '0.999' => 3.707,],
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27 => ['0' => 0.000, '0.5' => 0.684, '0.6' => 0.855, '0.7' => 1.057, '0.8' => 1.314, '0.9' => 1.703, '0.95' => 2.052, '0.98' => 2.473, '0.99' => 2.771, '0.998' => 3.421, '0.999' => 3.690,],
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28 => ['0' => 0.000, '0.5' => 0.683, '0.6' => 0.855, '0.7' => 1.056, '0.8' => 1.313, '0.9' => 1.701, '0.95' => 2.048, '0.98' => 2.467, '0.99' => 2.763, '0.998' => 3.408, '0.999' => 3.674,],
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29 => ['0' => 0.000, '0.5' => 0.683, '0.6' => 0.854, '0.7' => 1.055, '0.8' => 1.311, '0.9' => 1.699, '0.95' => 2.045, '0.98' => 2.462, '0.99' => 2.756, '0.998' => 3.396, '0.999' => 3.659,],
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30 => ['0' => 0.000, '0.5' => 0.683, '0.6' => 0.854, '0.7' => 1.055, '0.8' => 1.310, '0.9' => 1.697, '0.95' => 2.042, '0.98' => 2.457, '0.99' => 2.750, '0.998' => 3.385, '0.999' => 3.646,],
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40 => ['0' => 0.000, '0.5' => 0.681, '0.6' => 0.851, '0.7' => 1.050, '0.8' => 1.303, '0.9' => 1.684, '0.95' => 2.021, '0.98' => 2.423, '0.99' => 2.704, '0.998' => 3.307, '0.999' => 3.551,],
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60 => ['0' => 0.000, '0.5' => 0.679, '0.6' => 0.848, '0.7' => 1.045, '0.8' => 1.296, '0.9' => 1.671, '0.95' => 2.000, '0.98' => 2.390, '0.99' => 2.660, '0.998' => 3.232, '0.999' => 3.460,],
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80 => ['0' => 0.000, '0.5' => 0.678, '0.6' => 0.846, '0.7' => 1.043, '0.8' => 1.292, '0.9' => 1.664, '0.95' => 1.990, '0.98' => 2.374, '0.99' => 2.639, '0.998' => 3.195, '0.999' => 3.416,],
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100 => ['0' => 0.000, '0.5' => 0.677, '0.6' => 0.845, '0.7' => 1.042, '0.8' => 1.290, '0.9' => 1.660, '0.95' => 1.984, '0.98' => 2.364, '0.99' => 2.626, '0.998' => 3.174, '0.999' => 3.390,],
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1000 => ['0' => 0.000, '0.5' => 0.675, '0.6' => 0.842, '0.7' => 1.037, '0.8' => 1.282, '0.9' => 1.646, '0.95' => 1.962, '0.98' => 2.330, '0.99' => 2.581, '0.998' => 3.098, '0.999' => 3.300,],
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];
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/**
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* Get expected value.
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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 getMean() : int
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{
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return 0;
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}
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/**
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* Get median.
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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 getMedian() : int
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{
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return 0;
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}
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/**
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* Get mode.
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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
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{
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return 0;
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}
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/**
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* Get skewness.
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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 getSkewness() : int
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{
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return 0;
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}
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/**
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* Get variance.
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*
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* @param int $nu 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 $nu) : float
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{
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return $nu < 3 ? \PHP_FLOAT_MAX : $nu / ($nu - 2);
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}
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/**
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* Get standard deviation.
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*
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* @param int $nu 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 getStandardDeviation(int $nu) : float
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{
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return $nu < 3 ? \PHP_FLOAT_MAX : \sqrt(self::getVariance($nu));
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}
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/**
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* Get Ex. kurtosis.
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*
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* @param float $nu 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(float $nu) : float
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{
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return $nu < 5 && $nu > 2 ? \PHP_FLOAT_MAX : 6 / ($nu - 4);
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}
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}
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