diff --git a/Math/Statistic/MeasureOfDispersion.php b/Math/Statistic/MeasureOfDispersion.php index ea7e5b7ac..4481a6b1d 100644 --- a/Math/Statistic/MeasureOfDispersion.php +++ b/Math/Statistic/MeasureOfDispersion.php @@ -61,7 +61,7 @@ class MeasureOfDispersion * * @since 1.0.0 */ - public static function empiricalVariationcoefficient(array $values) : float + public static function empiricalVariationCoefficient(array $values) : float { $mean = Average::arithmeticMean($values); @@ -76,6 +76,8 @@ class MeasureOfDispersion * Calculage standard deviation. * * Example: ([4, 5, 9, 1, 3]) + * + * @latex \sigma = \sqrt{\sigma^{2}} = \sqrt{Var(X)} * * @param array $values Values * @@ -97,8 +99,12 @@ class MeasureOfDispersion /** * Calculage sample variance. + * + * Similar to `empiricalVariance`. * * Example: ([4, 5, 9, 1, 3]) + * + * @latex \sigma^{2} = Var(X) = \frac{1}{N - 1} \sum_{i = 1}^{N}\left(x_{i} - \bar{X}\right)^{2} * * @param array $values Values * @@ -121,8 +127,12 @@ class MeasureOfDispersion /** * Calculage empirical variance. + * + * Similar to `sampleVariance`. * * Example: ([4, 5, 9, 1, 3]) + * + * @latex \sigma^{2} = Var(X) = \frac{1}{N} \sum_{i = 1}^{N}\left(x_{i} - \bar{X}\right)^{2} * * @param array $values Values * @param array $probabilities Probabilities @@ -156,6 +166,8 @@ class MeasureOfDispersion * Calculage empirical covariance. * * Example: ([4, 5, 9, 1, 3], [4, 5, 9, 1, 3]) + * + * @latex \sigma_{XY} = cov(X, Y) = \sum_{i = 1}^{N}\frac{\left(x_{i} - \bar{X}\right) \left(y_{i} - \bar{Y}\right)}{N - 1} * * @param array $x Values * @param array $y Values