On the applications of aleph (ℵ)-function in a slightly different type-2 beta density model

Abstract

In the present paper, the author has studied about the structures which are the products and ratios of statistically independently distributed positive real scalar random variables.The author has derived the exact density of a slightly different Type-2 beta density by the Mellin Transform and Hankel Transform of the unknown density and afterthat the unknown density has been derived in terms of Aleph- functions by taking the inverse Mellin transform and Inverse Hankel Transform .A more general structure of Type-2 beta density has also been discussed. Some special cases in terms of I -function are also given.