A METHOD OF OBTAINING DISTRIBUTIONS OF TRANSFORMED RANDOM VARIABLES BY USING THE HEAVISIDE AND THE DIRAC GENERALIZED FUNCTIONS

Abstract

Chi AU and Judy TAM in [1] and Samia WAHED and M.Masoom ALI in [2]
compared the method of using the Dirac generalized function [3], [4] with the
conventional Change of Variable Technique of transformed continuous random
variables for several distributions. In the present article, we have applied the
concept of generalized probability density function based on the Heaviside and
the Dirac generalized functions for transformed random variables to obtain the
distributions of several transformed discrete and continuous random variables.
Moreover, we give a theorem for obtaining the joint distribution of a system of
transformed continuous random variables and some of its applications.