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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 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Math\Stochastic\Distribution; |
| 16 | |
| 17 | use phpOMS\Math\Functions\Gamma; |
| 18 | |
| 19 | /** |
| 20 | * Gamma 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 | */ |
| 27 | final class GammaDistribution |
| 28 | { |
| 29 | /** |
| 30 | * Get probability density function for shape and scale. |
| 31 | * |
| 32 | * @param float $x Value x |
| 33 | * @param float $k k shape |
| 34 | * @param float $theta Theta scale |
| 35 | * |
| 36 | * @return float |
| 37 | * |
| 38 | * @since 1.0.0 |
| 39 | */ |
| 40 | public static function getPdfScale(float $x, float $k, float $theta) : float |
| 41 | { |
| 42 | return 1 / (Gamma::gamma($k) * $theta ** $k) * \pow($x, $k - 1) * \exp(-$x / $theta); |
| 43 | } |
| 44 | |
| 45 | /** |
| 46 | * Get probability density function for shape and rate. |
| 47 | * |
| 48 | * @param float $x Value x |
| 49 | * @param float $alpha Alpha shape |
| 50 | * @param float $beta Beta rate |
| 51 | * |
| 52 | * @return float |
| 53 | * |
| 54 | * @since 1.0.0 |
| 55 | */ |
| 56 | public static function getPdfRate(float $x, float $alpha, float $beta) : float |
| 57 | { |
| 58 | return $beta ** $alpha / Gamma::gamma($alpha) * \pow($x, $alpha - 1) * \exp(-$beta * $x); |
| 59 | } |
| 60 | |
| 61 | /** |
| 62 | * Get probability density function for shape and scale. |
| 63 | * |
| 64 | * @param float $x Value x |
| 65 | * @param int $k k shape |
| 66 | * @param float $theta Theta scale |
| 67 | * |
| 68 | * @return float |
| 69 | * |
| 70 | * @since 1.0.0 |
| 71 | */ |
| 72 | public static function getPdfIntegerScale(float $x, int $k, float $theta) : float |
| 73 | { |
| 74 | return 1 / (Gamma::getGammaInteger($k) * $theta ** $k) * \pow($x, $k - 1) * \exp(-$x / $theta); |
| 75 | } |
| 76 | |
| 77 | /** |
| 78 | * Get probability density function for shape and rate. |
| 79 | * |
| 80 | * @param float $x Value x |
| 81 | * @param int $alpha Alpha shape |
| 82 | * @param float $beta Beta rate |
| 83 | * |
| 84 | * @return float |
| 85 | * |
| 86 | * @since 1.0.0 |
| 87 | */ |
| 88 | public static function getPdfIntegerRate(float $x, int $alpha, float $beta) : float |
| 89 | { |
| 90 | return $beta ** $alpha / Gamma::getGammaInteger($alpha) * \pow($x, $alpha - 1) * \exp(-$beta * $x); |
| 91 | } |
| 92 | |
| 93 | /** |
| 94 | * Get cumulative density function for shape and scale. |
| 95 | * |
| 96 | * @param float $x Value x |
| 97 | * @param float $k k shape |
| 98 | * @param float $theta Theta scale |
| 99 | * |
| 100 | * @return float |
| 101 | * |
| 102 | * @since 1.0.0 |
| 103 | */ |
| 104 | public static function getCdfScale(float $x, float $k, float $theta) : float |
| 105 | { |
| 106 | return 1 / Gamma::gamma($k) * Gamma::incompleteGammaFirst($k, $x / $theta); |
| 107 | } |
| 108 | |
| 109 | /** |
| 110 | * Get cumulative density function for shape and rate. |
| 111 | * |
| 112 | * @param float $x Value x |
| 113 | * @param float $alpha Alpha shape |
| 114 | * @param float $beta Beta rate |
| 115 | * |
| 116 | * @return float |
| 117 | * |
| 118 | * @since 1.0.0 |
| 119 | */ |
| 120 | public static function getCdfRate(float $x, float $alpha, float $beta) : float |
| 121 | { |
| 122 | return 1 / Gamma::gamma($alpha) * Gamma::incompleteGammaFirst($alpha, $beta * $x); |
| 123 | } |
| 124 | |
| 125 | /** |
| 126 | * Get expected value. |
| 127 | * |
| 128 | * @param float $k k shape |
| 129 | * @param float $theta Theta scale |
| 130 | * |
| 131 | * @return float |
| 132 | * |
| 133 | * @since 1.0.0 |
| 134 | */ |
| 135 | public static function getMeanScale(float $k, float $theta) : float |
| 136 | { |
| 137 | return $k * $theta; |
| 138 | } |
| 139 | |
| 140 | /** |
| 141 | * Get expected value. |
| 142 | * |
| 143 | * @param float $alpha Alpha shape |
| 144 | * @param float $beta Beta rate |
| 145 | * |
| 146 | * @return float |
| 147 | * |
| 148 | * @since 1.0.0 |
| 149 | */ |
| 150 | public static function getMeanRate(float $alpha, float $beta) : float |
| 151 | { |
| 152 | return $alpha / $beta; |
| 153 | } |
| 154 | |
| 155 | /** |
| 156 | * Get mode. |
| 157 | * |
| 158 | * @param float $k k shape |
| 159 | * @param float $theta Theta scale |
| 160 | * |
| 161 | * @return float |
| 162 | * |
| 163 | * @since 1.0.0 |
| 164 | */ |
| 165 | public static function getModeScale(float $k, float $theta) : float |
| 166 | { |
| 167 | return ($k - 1) * $theta; |
| 168 | } |
| 169 | |
| 170 | /** |
| 171 | * Get mode. |
| 172 | * |
| 173 | * @param float $alpha Alpha shape |
| 174 | * @param float $beta Beta scale |
| 175 | * |
| 176 | * @return float |
| 177 | * |
| 178 | * @since 1.0.0 |
| 179 | */ |
| 180 | public static function getModeRate(float $alpha, float $beta) : float |
| 181 | { |
| 182 | return ($alpha - 1) / $beta; |
| 183 | } |
| 184 | |
| 185 | /** |
| 186 | * Get skewness. |
| 187 | * |
| 188 | * @param float $k Shape k or alpha |
| 189 | * |
| 190 | * @return float |
| 191 | * |
| 192 | * @since 1.0.0 |
| 193 | */ |
| 194 | public static function getSkewness(float $k) : float |
| 195 | { |
| 196 | return 2 / \sqrt($k); |
| 197 | } |
| 198 | |
| 199 | /** |
| 200 | * Get Ex. kurtosis. |
| 201 | * |
| 202 | * @param float $k Shape k or alpha |
| 203 | * |
| 204 | * @return float |
| 205 | * |
| 206 | * @since 1.0.0 |
| 207 | */ |
| 208 | public static function getExKurtosis(float $k) : float |
| 209 | { |
| 210 | return 6 / $k; |
| 211 | } |
| 212 | |
| 213 | /** |
| 214 | * Get variance. |
| 215 | * |
| 216 | * @param float $k k shape |
| 217 | * @param float $theta Theta scale |
| 218 | * |
| 219 | * @return float |
| 220 | * |
| 221 | * @since 1.0.0 |
| 222 | */ |
| 223 | public static function getVarianceScale(float $k, float $theta) : float |
| 224 | { |
| 225 | return $k * $theta ** 2; |
| 226 | } |
| 227 | |
| 228 | /** |
| 229 | * Get standard deviation. |
| 230 | * |
| 231 | * @param float $k k shape |
| 232 | * @param float $theta Theta scale |
| 233 | * |
| 234 | * @return float |
| 235 | * |
| 236 | * @since 1.0.0 |
| 237 | */ |
| 238 | public static function getStandardDeviationScale(float $k, float $theta) : float |
| 239 | { |
| 240 | return \sqrt(self::getVarianceScale($k, $theta)); |
| 241 | } |
| 242 | |
| 243 | /** |
| 244 | * Get variance. |
| 245 | * |
| 246 | * @param float $alpha Alpha shape |
| 247 | * @param float $beta Beta scale |
| 248 | * |
| 249 | * @return float |
| 250 | * |
| 251 | * @since 1.0.0 |
| 252 | */ |
| 253 | public static function getVarianceRate(float $alpha, float $beta) : float |
| 254 | { |
| 255 | return $alpha / ($beta ** 2); |
| 256 | } |
| 257 | |
| 258 | /** |
| 259 | * Get standard deviation. |
| 260 | * |
| 261 | * @param float $alpha Alpha shape |
| 262 | * @param float $beta Beta scale |
| 263 | * |
| 264 | * @return float |
| 265 | * |
| 266 | * @since 1.0.0 |
| 267 | */ |
| 268 | public static function getStandardDeviationRate(float $alpha, float $beta) : float |
| 269 | { |
| 270 | return \sqrt(self::getVarianceRate($alpha, $beta)); |
| 271 | } |
| 272 | |
| 273 | /** |
| 274 | * Get moment generating function. |
| 275 | * |
| 276 | * @param float $k k shape |
| 277 | * @param float $t Value t |
| 278 | * @param float $theta Theta scale |
| 279 | * |
| 280 | * @return float |
| 281 | * |
| 282 | * @since 1.0.0 |
| 283 | */ |
| 284 | public static function getMgfScale(float $k, float $t, float $theta) : float |
| 285 | { |
| 286 | return \pow(1 - $theta * $t, -$k); |
| 287 | } |
| 288 | |
| 289 | /** |
| 290 | * Get moment generating function. |
| 291 | * |
| 292 | * @param float $t Value t |
| 293 | * @param float $alpha Alpha shape |
| 294 | * @param float $beta Beta scale |
| 295 | * |
| 296 | * @return float |
| 297 | * |
| 298 | * @since 1.0.0 |
| 299 | */ |
| 300 | public static function getMgfRate(float $t, float $alpha, float $beta) : float |
| 301 | { |
| 302 | return \pow(1 - $t / $beta, -$alpha); |
| 303 | } |
| 304 | } |