Characterizations of Certain (2023-2024) Introduced Univariate Continuous Distributions III

Abstract

This paper is a continuation of our previous works with the same title, which deals with various characterizations of certain univariate continuous distributions proposed in (2023-2024) after the publication of our first two papers in (2024). These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) the hazard function; (iii) reverse hazard function and (iv) conditional expectation of a single function of the random variable. It should be mentioned that for the characterization (i) the cumulative distribution function need not have a closed form and depends on the solution of a first order differential equation, which provides a bridge between probability and differential equation.