> * @since 1.0.0 */ public const TABLE = [ 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], 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,], ]; /** * Get expected value. * * @return int * * @since 1.0.0 */ public static function getMean() : int { return 0; } /** * Get median. * * @return int * * @since 1.0.0 */ public static function getMedian() : int { return 0; } /** * Get mode. * * @return int * * @since 1.0.0 */ public static function getMode() : int { return 0; } /** * Get skewness. * * @return int * * @since 1.0.0 */ public static function getSkewness() : int { return 0; } /** * Get variance. * * @param int $nu Degrees of freedom * * @return float * * @since 1.0.0 */ public static function getVariance(int $nu) : float { return $nu < 3 ? \PHP_FLOAT_MAX : $nu / ($nu - 2); } /** * Get standard deviation. * * @param int $nu Degrees of freedom * * @return float * * @since 1.0.0 */ public static function getStandardDeviation(int $nu) : float { return $nu < 3 ? \PHP_FLOAT_MAX : \sqrt(self::getVariance($nu)); } /** * Get Ex. kurtosis. * * @param float $nu Degrees of freedom * * @return float * * @since 1.0.0 */ public static function getExKurtosis(float $nu) : float { return $nu < 5 && $nu > 2 ? \PHP_FLOAT_MAX : 6 / ($nu - 4); } /** * Get cummulative distribution function. * * @param float $x Value * @param int $degrees Degrees of freedom * @param int $tails Tails (1 or 2) * * @return float * * @since 1.0.0 */ public static function getCdf(float $x, int $degrees, int $tails = 2) : float { if ($x < 0.0 || $degrees < 1 || $tails < 1 || $tails > 2) { return 0.0; } /** * "AS 3" by B E Cooper of the Atlas Computer Laboratory * Ellis Horwood Ltd.; W. Sussex, England */ $term = $degrees; $theta = \atan2($x, \sqrt($term)); $cos = \cos($theta); $sin = \sin($theta); $sum = 0.0; if ($degrees % 2 === 1) { $i = 3; $term = $cos; } else { $i = 2; $term = 1; } $sum = $term; while ($i < $degrees) { $term *= $cos ** 2 * ($i - 1) / $i; $sum += $term; $i += 2; } $sum *= $sin; if ($degrees % 2 === 1) { $sum = 2 / \M_PI * ($sum + $theta); } $t = 0.5 * (1 + $sum); return $tails === 1 ? 1 - \abs($t) : 1 - \abs(1 - $t - $t); } }