  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.
