TITLE:
Distributions of Ratios: From Random Variables to Random Matrices
AUTHORS:
Thu Pham-Gia, Noyan Turkkan
KEYWORDS:
Matrix Variate, Beta Distribution, Generalized-F Distribution, Ratios, Meijer G-Function, Wishart Distribution, Ratio
JOURNAL NAME:
Open Journal of Statistics,
Vol.1 No.2,
July
21,
2011
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.