Computation of the Generalized F Distribution

Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F distribution to mixtures of chi-squared variables. The distribution is given in terms of the Lauricella functions. The truncation error bounds are given in terms of hypergeometric functions. Applications to detecting joint outliers and Hotelling's misspecified T^2 distribution are given.