Characterizations of Recently Introduced Continuous Distributions III


G.G. Hamedani, PhD – Marquette University, Madison, Wisconsin, USA

Series: Mathematics Research Developments

BISAC: MAT029000

This monograph is, as far as the author has gathered, the third one of its kind which presents various characterizations of many important continuous distributions. It consists of two chapters. The first chapter lists cumulative distributions and probability density functions of six hundred and sixty seven newly proposed univariate continuous distributions. Chapter Two consists of four sections. Section 2.1 provides characterizations of the majority of the distributions mentioned in Chapter One, based on the ratio of two truncated moments. Section 2.2 takes up the characterizations of some of these distributions in terms of their hazard functions. Section 2.3 deals with the characterizations some of these distributions based on their reverse hazard functions. Characterizations of some of these distributions based on the conditional expectations of certain functions of the random variable are presented in Section 2.4. As pointed out in our previous Monographs (I & II), a good number of proposed distributions in this volume have already been introduced in the literature.

Table of Contents


Chapter 1. Introduction

Section 1.1: Preliminaries

Chapter 2. Characterizations of distributions

Section 2.1: Characterizations based on two truncated moments

Section 2.2: Characterization in terms of hazard function

Section 2.3: Characterization in terms of the reverse (or reversed) hazard function

Section 2.4: Characterization based on the conditional expectation of certain function of the random variable

Appendix A


Additional information



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