Distributions of Ratios: From Random Variables to Random Matrices

Abstract

The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its defini-tion, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its repro-ductive property.Keywords: Matrix Variate, Beta Distribution, Generalized-F Distribution, Ratios, Meijer G-Function, Wishart Distribution, Ratio