Distributions of Ratios: From Random Variables to Random Matrices

Thu Pham-Gia, Noyan Turkkan

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Dept of Mathematics and Statistics, Universite de Moncton, Canada.

DOI: 10.4236/ojs.2011.12011                

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 definition, 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 reproductive property.

Keywords

Matrix Variate, Beta Distribution, Generalized-F Distribution, Ratios, Meijer G-Function, Wishart Distribution, Ratio

Conflicts of Interest

The authors declare no conflicts of interest.

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