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Add latex formulas

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This commit is contained in:
Dennis Eichhorn 2018-02-22 21:12:36 +01:00
parent 510842727c
commit cb374f663a
1 changed files with 13 additions and 1 deletions
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14
Math/Statistic/MeasureOfDispersion.php
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@ -61,7 +61,7 @@ class MeasureOfDispersion
* *
* @since 1.0.0 * @since 1.0.0
*/ */
public static function empiricalVariationcoefficient(array $values) : float public static function empiricalVariationCoefficient(array $values) : float
{ {
$mean = Average::arithmeticMean($values); $mean = Average::arithmeticMean($values);
@ -77,6 +77,8 @@ class MeasureOfDispersion
* *
* Example: ([4, 5, 9, 1, 3]) * Example: ([4, 5, 9, 1, 3])
* *
* @latex \sigma = \sqrt{\sigma^{2}} = \sqrt{Var(X)}
*
* @param array $values Values * @param array $values Values
* *
* @return float * @return float
@ -98,8 +100,12 @@ class MeasureOfDispersion
/** /**
* Calculage sample variance. * Calculage sample variance.
* *
* Similar to `empiricalVariance`.
*
* Example: ([4, 5, 9, 1, 3]) * 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 * @param array $values Values
* *
* @return float * @return float
@ -122,8 +128,12 @@ class MeasureOfDispersion
/** /**
* Calculage empirical variance. * Calculage empirical variance.
* *
* Similar to `sampleVariance`.
*
* Example: ([4, 5, 9, 1, 3]) * 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 $values Values
* @param array $probabilities Probabilities * @param array $probabilities Probabilities
* *
@ -157,6 +167,8 @@ class MeasureOfDispersion
* *
* Example: ([4, 5, 9, 1, 3], [4, 5, 9, 1, 3]) * 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 $x Values
* @param array $y Values * @param array $y Values
* *