A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. Let and be independent variates distributed as chi-squared with and degrees of freedom.
Define a statistic as the ratio of the dispersions of the two distributions
(1)
|
This statistic then has an -distribution on domain with probability function and cumulative distribution function given by
(2)
| |||
(3)
| |||
(4)
| |||
(5)
|
where is the gamma function, is the beta function, is the regularized beta function, and is a hypergeometric function.
The -distribution is implemented in the Wolfram Language as FRatioDistribution[n, m].
The mean, variance, skewness and kurtosis excess are
(6)
| |||
(7)
| |||
(8)
| |||
(9)
|
The probability that would be as large as it is if the first distribution has a smaller variance than the second is denoted .