Resumen de Some properties of beta functions and the distribution for the product of independent beta random variables

Giorgio Pederzoli

• Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration, the exact null density of Wilks'? for testing linear hypothesis in the real Gaussian case is derived. Furthermore, it will be shown that this method is applicable also to problems of a more general nature.