Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -III

TL;DR

This paper extends Kober fractional integral operators to multivariable cases using statistical techniques, providing new interpretations in terms of joint densities for dependent and independent random variable sets.

Contribution

It introduces a multivariable extension of Kober operators with statistical interpretations, considering dependent and independent random variable sets.

Findings

Defined multivariable Kober fractional integral operators.

Provided statistical interpretations in terms of joint densities.

Extended the operators to dependent and independent variable sets.

Abstract

In this article we define Kober fractional integral operators in the multivariable case. First we consider one sequence of independent random variables and an arbitrary function, which can act as the joint density of another sequence of random variables. Then we define a concept, analogous to the concept of Kober operators in the scalar variable case. This extension is achieved by using statistical techniques and the representation gives an interpretation in terms of a joint statistical density. Then we look at two sets of random variables where between the sets they are independently distributed but within each set they are dependent. Again extensions of Kober fractional integral operator are considered. Several such statistical interpretations are given for Kober operators in the multivariable case.