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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Statistic |
| 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\Statistic; |
| 16 | |
| 17 | use phpOMS\Math\Exception\ZeroDivisionException; |
| 18 | use phpOMS\Math\Matrix\Exception\InvalidDimensionException; |
| 19 | |
| 20 | /** |
| 21 | * Measure of dispersion. |
| 22 | * |
| 23 | * @package phpOMS\Math\Statistic |
| 24 | * @license OMS License 2.0 |
| 25 | * @link https://jingga.app |
| 26 | * @since 1.0.0 |
| 27 | */ |
| 28 | final class MeasureOfDispersion |
| 29 | { |
| 30 | /** |
| 31 | * Constructor. |
| 32 | * |
| 33 | * @since 1.0.0 |
| 34 | * @codeCoverageIgnore |
| 35 | */ |
| 36 | private function __construct() |
| 37 | { |
| 38 | } |
| 39 | |
| 40 | /** |
| 41 | * Get range. |
| 42 | * |
| 43 | * Example: ([4, 5, 9, 1, 3]) |
| 44 | * |
| 45 | * @param array<int, int|float> $values Values |
| 46 | * |
| 47 | * @return float |
| 48 | * |
| 49 | * @since 1.0.0 |
| 50 | */ |
| 51 | public static function range(array $values) : float |
| 52 | { |
| 53 | \sort($values); |
| 54 | $end = \end($values); |
| 55 | $start = \reset($values); |
| 56 | |
| 57 | return $end - $start; |
| 58 | } |
| 59 | |
| 60 | /** |
| 61 | * Calculage empirical variation coefficient. |
| 62 | * |
| 63 | * Example: ([4, 5, 9, 1, 3]) |
| 64 | * |
| 65 | * @param array<int, int|float> $values Values |
| 66 | * @param float $mean Mean |
| 67 | * |
| 68 | * @return float |
| 69 | * |
| 70 | * @throws ZeroDivisionException This exception is thrown if the mean is 0 |
| 71 | * |
| 72 | * @since 1.0.0 |
| 73 | */ |
| 74 | public static function empiricalVariationCoefficient(array $values, float $mean = null) : float |
| 75 | { |
| 76 | $mean = $mean !== null ? $mean : Average::arithmeticMean($values); |
| 77 | |
| 78 | if ($mean === 0.0) { |
| 79 | throw new ZeroDivisionException(); |
| 80 | } |
| 81 | |
| 82 | return self::standardDeviationSample($values) / $mean; |
| 83 | } |
| 84 | |
| 85 | /** |
| 86 | * Calculate standard deviation of sample. |
| 87 | * |
| 88 | * Example: ([4, 5, 9, 1, 3]) |
| 89 | * |
| 90 | * @latex \sigma = \sqrt{\sigma^{2}} = \sqrt{Var(X)} |
| 91 | * |
| 92 | * @param array<int, int|float> $values Values |
| 93 | * @param float $mean Mean |
| 94 | * |
| 95 | * @return float |
| 96 | * |
| 97 | * @since 1.0.0 |
| 98 | */ |
| 99 | public static function standardDeviationSample(array $values, float $mean = null) : float |
| 100 | { |
| 101 | $mean = $mean !== null ? $mean : Average::arithmeticMean($values); |
| 102 | $sum = 0.0; |
| 103 | |
| 104 | $valueCount = 0; |
| 105 | |
| 106 | foreach ($values as $value) { |
| 107 | $sum += ($value - $mean) ** 2; |
| 108 | ++$valueCount; |
| 109 | } |
| 110 | |
| 111 | return \sqrt($sum / ($valueCount - 1)); |
| 112 | } |
| 113 | |
| 114 | /** |
| 115 | * Calculate standard deviation of entire population |
| 116 | * |
| 117 | * Example: ([4, 5, 9, 1, 3]) |
| 118 | * |
| 119 | * @latex \sigma = \sqrt{\sigma^{2}} = \sqrt{Var(X)} |
| 120 | * |
| 121 | * @param array<int, int|float> $values Values |
| 122 | * @param float $mean Mean |
| 123 | * |
| 124 | * @return float |
| 125 | * |
| 126 | * @since 1.0.0 |
| 127 | */ |
| 128 | public static function standardDeviationPopulation(array $values, float $mean = null) : float |
| 129 | { |
| 130 | $mean = $mean !== null ? $mean : Average::arithmeticMean($values); |
| 131 | $sum = 0.0; |
| 132 | |
| 133 | $valueCount = 0; |
| 134 | |
| 135 | foreach ($values as $value) { |
| 136 | $sum += ($value - $mean) ** 2; |
| 137 | ++$valueCount; |
| 138 | } |
| 139 | |
| 140 | return \sqrt($sum / $valueCount); |
| 141 | } |
| 142 | |
| 143 | /** |
| 144 | * Calculage sample variance. |
| 145 | * |
| 146 | * Similar to `empiricalVariance`. |
| 147 | * |
| 148 | * Example: ([4, 5, 9, 1, 3]) |
| 149 | * |
| 150 | * @latex \sigma^{2} = Var(X) = \frac{1}{N - 1} \sum_{i = 1}^{N}\left(x_{i} - \bar{X}\right)^{2} |
| 151 | * |
| 152 | * @param array<int, int|float> $values Values |
| 153 | * @param float $mean Mean |
| 154 | * |
| 155 | * @return float |
| 156 | * |
| 157 | * @throws ZeroDivisionException This exception is thrown if the size of the values array is less than 2 |
| 158 | * |
| 159 | * @since 1.0.0 |
| 160 | */ |
| 161 | public static function sampleVariance(array $values, float $mean = null) : float |
| 162 | { |
| 163 | $count = \count($values); |
| 164 | |
| 165 | if ($count < 2) { |
| 166 | throw new ZeroDivisionException(); |
| 167 | } |
| 168 | |
| 169 | return self::empiricalVariance($values, [], $mean) * $count / ($count - 1); |
| 170 | } |
| 171 | |
| 172 | /** |
| 173 | * Calculage empirical variance. |
| 174 | * |
| 175 | * Similar to `sampleVariance`. |
| 176 | * |
| 177 | * Example: ([4, 5, 9, 1, 3]) |
| 178 | * |
| 179 | * @latex \sigma^{2} = Var(X) = \frac{1}{N} \sum_{i = 1}^{N}\left(x_{i} - \bar{X}\right)^{2} |
| 180 | * |
| 181 | * @param array<int, int|float> $values Values |
| 182 | * @param array<int, int|float> $probabilities Probabilities |
| 183 | * @param float $mean Mean |
| 184 | * |
| 185 | * @return float |
| 186 | * |
| 187 | * @throws ZeroDivisionException This exception is thrown if the values array is empty |
| 188 | * |
| 189 | * @since 1.0.0 |
| 190 | */ |
| 191 | public static function empiricalVariance(array $values, array $probabilities = [], float $mean = null) : float |
| 192 | { |
| 193 | $count = \count($values); |
| 194 | $hasProbability = !empty($probabilities); |
| 195 | |
| 196 | if ($count === 0) { |
| 197 | throw new ZeroDivisionException(); |
| 198 | } |
| 199 | |
| 200 | $mean = $hasProbability ? Average::weightedAverage($values, $probabilities) : ($mean !== null ? $mean : Average::arithmeticMean($values)); |
| 201 | $sum = 0; |
| 202 | |
| 203 | foreach ($values as $key => $value) { |
| 204 | $sum += ($hasProbability ? $probabilities[$key] : 1) * ($value - $mean) ** 2; |
| 205 | } |
| 206 | |
| 207 | return $hasProbability ? $sum : $sum / $count; |
| 208 | } |
| 209 | |
| 210 | /** |
| 211 | * Calculage empirical covariance. |
| 212 | * |
| 213 | * Example: ([4, 5, 9, 1, 3], [4, 5, 9, 1, 3]) |
| 214 | * |
| 215 | * @latex cov(X,Y) = \frac{1}{N} \sum_{i = 1}^{N}\left(x_{i} - \bar{X}\right)\left(y_{i} - \bar{Y}\right) |
| 216 | * |
| 217 | * @param array<int, int|float> $x Values |
| 218 | * @param array<int, int|float> $y Values |
| 219 | * @param float $meanX Mean |
| 220 | * @param float $meanY Mean |
| 221 | * |
| 222 | * @return float |
| 223 | * |
| 224 | * @throws ZeroDivisionException This exception is thrown if the size of the x array is less than 2 |
| 225 | * @throws InvalidDimensionException This exception is thrown if x and y have different dimensions |
| 226 | * |
| 227 | * @since 1.0.0 |
| 228 | */ |
| 229 | public static function empiricalCovariance(array $x, array $y, float $meanX = null, float $meanY = null) : float |
| 230 | { |
| 231 | $count = \count($x); |
| 232 | |
| 233 | if ($count < 2) { |
| 234 | throw new ZeroDivisionException(); |
| 235 | } |
| 236 | |
| 237 | if ($count !== \count($y)) { |
| 238 | throw new InvalidDimensionException($count . 'x' . \count($y)); |
| 239 | } |
| 240 | |
| 241 | $xMean = $meanX !== null ? $meanX : Average::arithmeticMean($x); |
| 242 | $yMean = $meanY !== null ? $meanY : Average::arithmeticMean($y); |
| 243 | |
| 244 | $sum = 0.0; |
| 245 | |
| 246 | for ($i = 0; $i < $count; ++$i) { |
| 247 | $sum += ($x[$i] - $xMean) * ($y[$i] - $yMean); |
| 248 | } |
| 249 | |
| 250 | return $sum / $count; |
| 251 | } |
| 252 | |
| 253 | /** |
| 254 | * Calculage empirical covariance on a sample |
| 255 | * |
| 256 | * Example: ([4, 5, 9, 1, 3], [4, 5, 9, 1, 3]) |
| 257 | * |
| 258 | * @latex cov(X,Y) = \frac{1}{N - 1} \sum_{i = 1}^{N}\left(x_{i} - \bar{X}\right)\left(y_{i} - \bar{Y}\right) |
| 259 | * |
| 260 | * @param array<int, int|float> $x Values |
| 261 | * @param array<int, int|float> $y Values |
| 262 | * @param float $meanX Mean |
| 263 | * @param float $meanY Mean |
| 264 | * |
| 265 | * @return float |
| 266 | * |
| 267 | * @throws ZeroDivisionException This exception is thrown if the size of the x array is less than 2 |
| 268 | * |
| 269 | * @since 1.0.0 |
| 270 | */ |
| 271 | public static function sampleCovariance(array $x, array $y, float $meanX = null, float $meanY = null) : float |
| 272 | { |
| 273 | $count = \count($x); |
| 274 | |
| 275 | if ($count < 2) { |
| 276 | throw new ZeroDivisionException(); |
| 277 | } |
| 278 | |
| 279 | return self::empiricalCovariance($x, $y, $meanX, $meanY) * $count / ($count - 1); |
| 280 | } |
| 281 | |
| 282 | /** |
| 283 | * Get interquartile range. |
| 284 | * |
| 285 | * @param array<int, int|float> $x Dataset |
| 286 | * |
| 287 | * @return float |
| 288 | * |
| 289 | * @since 1.0.0 |
| 290 | */ |
| 291 | public static function getIQR(array $x) : float |
| 292 | { |
| 293 | $count = \count($x); |
| 294 | |
| 295 | if ($count % 2 !== 0) { |
| 296 | --$count; |
| 297 | } |
| 298 | |
| 299 | /** @var int $count */ |
| 300 | $count /= 2; |
| 301 | |
| 302 | \sort($x); |
| 303 | |
| 304 | $Q1 = Average::median(\array_slice($x, 0, $count)); |
| 305 | $Q3 = Average::median(\array_slice($x, -$count, $count)); |
| 306 | |
| 307 | return $Q3 - $Q1; |
| 308 | } |
| 309 | |
| 310 | /** |
| 311 | * Get mean deviation. |
| 312 | * |
| 313 | * @param array<int, int|float> $x Values |
| 314 | * @param float $mean Mean |
| 315 | * @param int $offset Population/Size offset |
| 316 | * |
| 317 | * @return float |
| 318 | * |
| 319 | * @since 1.0.0 |
| 320 | */ |
| 321 | public static function meanDeviation(array $x, float $mean = null, int $offset = 0) : float |
| 322 | { |
| 323 | $mean = $mean !== null ? $mean : Average::arithmeticMean($x); |
| 324 | $sum = 0.0; |
| 325 | |
| 326 | foreach ($x as $xi) { |
| 327 | $sum += ($xi - $mean); |
| 328 | } |
| 329 | |
| 330 | return $sum / (\count($x) - $offset); |
| 331 | } |
| 332 | |
| 333 | /** |
| 334 | * Get the deviation to the mean |
| 335 | * |
| 336 | * @param array<int, int|float> $x Values |
| 337 | * |
| 338 | * @return array |
| 339 | * |
| 340 | * @since 1.0.0 |
| 341 | */ |
| 342 | public static function meanDeviationArray(array $x, float $mean = null) : array |
| 343 | { |
| 344 | $mean = $mean !== null ? $mean : Average::arithmeticMean($x); |
| 345 | |
| 346 | foreach ($x as $key => $value) { |
| 347 | $x[$key] = $value - $mean; |
| 348 | } |
| 349 | |
| 350 | return $x; |
| 351 | } |
| 352 | |
| 353 | /** |
| 354 | * Get mean absolute deviation (MAD). |
| 355 | * |
| 356 | * @param array<int, int|float> $x Values |
| 357 | * @param float $mean Mean |
| 358 | * @param int $offset Population/Size offset |
| 359 | * |
| 360 | * @return float |
| 361 | * |
| 362 | * @since 1.0.0 |
| 363 | */ |
| 364 | public static function meanAbsoluteDeviation(array $x, float $mean = null, int $offset = 0) : float |
| 365 | { |
| 366 | $mean = $mean !== null ? $mean : Average::arithmeticMean($x); |
| 367 | $sum = 0.0; |
| 368 | |
| 369 | foreach ($x as $xi) { |
| 370 | $sum += \abs($xi - $mean); |
| 371 | } |
| 372 | |
| 373 | return $sum / (\count($x) - $offset); |
| 374 | } |
| 375 | |
| 376 | /** |
| 377 | * Get the deviation to the mean |
| 378 | * |
| 379 | * @param array<int, int|float> $x Values |
| 380 | * |
| 381 | * @return array |
| 382 | * |
| 383 | * @since 1.0.0 |
| 384 | */ |
| 385 | public static function meanAbsoluteDeviationArray(array $x, float $mean = null) : array |
| 386 | { |
| 387 | $mean = $mean !== null ? $mean : Average::arithmeticMean($x); |
| 388 | |
| 389 | foreach ($x as $key => $value) { |
| 390 | $x[$key] = \abs($value - $mean); |
| 391 | } |
| 392 | |
| 393 | return $x; |
| 394 | } |
| 395 | |
| 396 | /** |
| 397 | * Get squared mean deviation. |
| 398 | * |
| 399 | * @param array<int, int|float> $x Values |
| 400 | * @param float $mean Mean |
| 401 | * @param int $offset Population/Size offset |
| 402 | * |
| 403 | * @return float |
| 404 | * |
| 405 | * @since 1.0.0 |
| 406 | */ |
| 407 | public static function squaredMeanDeviation(array $x, float $mean = null, int $offset = 0) : float |
| 408 | { |
| 409 | $mean = $mean !== null ? $mean : Average::arithmeticMean($x); |
| 410 | $sum = 0.0; |
| 411 | |
| 412 | foreach ($x as $xi) { |
| 413 | $sum += ($xi - $mean) ** 2; |
| 414 | } |
| 415 | |
| 416 | return $sum / (\count($x) - $offset); |
| 417 | } |
| 418 | |
| 419 | /** |
| 420 | * Get the deviation to the mean squared |
| 421 | * |
| 422 | * @param array<int, int|float> $x Values |
| 423 | * |
| 424 | * @return array |
| 425 | * |
| 426 | * @since 1.0.0 |
| 427 | */ |
| 428 | public static function squaredMeanDeviationArray(array $x, float $mean = null) : array |
| 429 | { |
| 430 | $mean = $mean !== null ? $mean : Average::arithmeticMean($x); |
| 431 | |
| 432 | foreach ($x as $key => $value) { |
| 433 | $x[$key] = ($value - $mean) ** 2; |
| 434 | } |
| 435 | |
| 436 | return $x; |
| 437 | } |
| 438 | } |