F-Distribution | f distributions
Acontinuousstatisticaldistributionwhicharisesinthetestingofwhethertwoobservedsampleshavethesamevariance[1].Letandbeindependentvariatesdistributedaschi-squared[2]withanddegreesoffreedom[3].Defineastatisticastheratioofthedispersionsofthetwodistributions(1)Thisstatisticthenhasan-distributionondomainwithprobabilityfunctionandcumulativedistributionfunctiongivenbywhereisthegammafunction[4],isthebetafunction[5],istheregularizedbetafunction[6],andisahypergeometricfunction[7].The-distributionisimplem...
A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance[1]. Let and be independent variates distributed as chi-squared[2] with and degrees of freedom[3].
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
where is the gamma function[4], is the beta function[5], is the regularized beta function[6], and is a hypergeometric function[7].
The -distribution is implemented in the Wolfram Language[8] as FRatioDistribution[9][n, m].
The mean[10], variance[11], skewness[12] and kurtosis excess[13] are
The probability that would be as large as it is if the first distribution has a smaller variance than the second is denoted .
SEE ALSO: Be...