If Y1 has a non-central chi-squared distribution with ν1 degrees of freedom and non-centrality parameter λ, and if Y2 is independent of Y1 and has a chi-squared distribution with ν2 degrees of freedom, then the ratio X, is said to have a non-central F-distribution with non-centrality parameter λ and with ν1 and ν2 degrees of freedom. The probability density function f of X is given by where B is the beta function. The distribution has mean and variance given by respectively (with ν2>4). The distribution is unimodal.
Subjects: Probability and Statistics.