Erdélyi-Kober fractional integral operators from a statistical perspective -II

Cogent Mathematics

A.M. Mathai¹  H.J. Haubold¹ 

[1] Centre for Mathematical and Statistical Sciences;

关键词: matrix-variate;    Erdélyi-Kober operators;    fractional integrals;    densities;    pathway models;   

DOI  :  10.1080/23311835.2017.1309769

来源: DOAJ

【 摘 要 】

In this paper we examine the densities of a product and a ratio of two real positive definite matrix-variate random variables $ X_1 $ and $ X_2 $, which are statistically independently distributed, and we consider the density of the product $ U_1=X_2^{\frac{1}{2}}X_1X_2^{\frac{1}{2}} $ as well as the density of the ratio $ U_2=X_2^{\frac{1}{2}}X_1^{-1}X_2^{\frac{1}{2}} $. We define matrix-variate Kober fractional integral operators of the first and second kinds from a statistical perspective, making use of the derivation in the predecessor of this paper for the scalar variable case, by deriving the densities of product cand ratios where one variable has a matrix-variate type-1 beta density and the other matrix variable has an arbitrary density, in the sense, any real-valued scalar function f(X) of matrix argument X, such that f(X) is non-negative for all X and the total integral over all X, on the support of f(X), is unity. A number of generalizations are considered, by using pathway models, by appending matrix variate hypergeometric series etc. During this process matrix-variate Saigo operator and other operators are also defined and properties studied.

【 授权许可】

Unknown