-Snedecor Dstribution
The Fisher–Snedecor distribution, also known as the F distribution, is a continuous probability distribution commonly used in inferential statistics. It is a right-skewed distribution, where the location of the mode is always to the left of the mean and median.
The Fisher–Snedecor distribution is parameterized by two degrees of freedom—the first (df1) and the second (df2). The PDF of the F distribution is:
f(x; df1, df2) = (df1/df2) (1/x)^((df1+df2)/2) * Gamma((df1+df2)/2) / (Gamma(df1/2) * Gamma(df2/2))
where x is a real number greater than zero and Gamma(x) is the Gamma function. The cumulative distribution function of the F distribution is:
F(x; df1, df2) = gamma_inc((df1/2), (df2/2), (df1/df2)x) / Gamma((df1+df2)/2)
where Gamma_inc(a,b,x) is the upper incomplete Gamma function and Gamma(x) is the Gamma function.