The exact distribution of the ratio of a linear combination of chi‐square variables over the root of a product of chi‐square variables
Serge B. Provost · Canadian Journal of Statistics · 1986
Abstract This article gives the exact distribution of a statistic whose numerator and denominator are independent, the former being a linear combination of independent chi‐square variables and the latter being thekth root of a product ofkindependent chi‐square variables. This structure appears in the study of multivariate linear functional relationship models. The technique of the inverse Mellin transform is used in order to obtain the density of this test statistic in a computable form.