Characterizations of Recently Introduced Univariate Continuous Distributions



Series: Mathematics Research Developments
BISAC: MAT029000

This monograph is, as far as the authors have gathered, the first one of its kind which presents various characterizations of many important and continuous distributions. It consists of six chapters. The first chapter lists cumulative distribution functions, probability density functions, hazard functions and reverse hazard functions of one hundred thirty-six important univariate continuous distributions. Chapter Two provides characterizations of these distributions based on the ratio of two truncated moments.

Chapter Three takes up the characterizations of some of these distributions in terms of their hazard functions. Chapter Four deals with the characterizations of 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 Chapter Five. Finally, to make this book self-contained, we present the characterizations of a large number of distributions (without their proofs) that have already been published by Hamedani and coauthors in Chapter Six.

Table of Contents

Table of Contents

Chapter 1. Introduction

Chapter 2. Characterizations Based on Two Truncated Moments

Chapter 3. Characterizations Based on Hazard Function

Chapter 4. Characterizations Based on Reverse Hazard Function

Chapter 5. Characterizations Based on Conditional Expectation

Chapter 6. Characterization Results Already Published by Hamedani and Coauthors


About the Authors



“The authors have put in tremendous intellectual efforts to come up with this compilation and it will undoubtedly serve as an Encyclopedia in this field of study. It is an amazing compilation of so many basic and derived (life) distributions and their characterizations. As we know characterization problems are themselves very intriguing and intellectually challenging. The authors have mastered the subject matter so much so that they have ventured into this difficult area in presenting a vast material with utmost technical competence. On behalf of the researchers in the area of life distributions and allied topics, I congratulate the authors. Simply told, this is a ‘Masterpiece’ in any sense of the term.” – Bikas K. Sinha, Professor of Statistics (Retired), Indian Statistical Institute, Kolkata, India

“To fully appreciate the meaning and the proper application of a continuous univariate distribution one should be equipped to go through two scientific steps: First Step: one should know the true meaning of the distribution by various available means of characterizations. Second Step: one should know the underlying phenomenon for which the distribution is to be meaningfully approximated. This outstanding book prepared by Professors G.G. Hamedani and M. Maadooliat is providing timely and most comprehensive mathematical/statistical tools for the First Step in applying and utilizing continuous univariate distributions.” – Samad Hedayat, UIC Distinguished Professor, Deptartment of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Illinois USA

“This volume will be of great value to researchers as they navigate the burgeoning literature on generalized univariate distributions. It will enable them to ruminate on possible variations of existing themes and to avoid rediscovering the wheel in some instances.” – Barry Charles Arnold, Distinguished Professor, Department of Statistics, University of California, Riverside, CA USA

“The excellent book of Professors G.G. Hamedani and M. Maadooliat is devoted to characterizations of a large number of recently published continuous univariate distributions. It covers characterizations of 136 recently published continuous univariate distributions. These characterizations are based on the ratio of two truncated moments, the hazard functions, the reverse hazard functions and the conditional expectations of certain functions. Beside these results, important results of the authors of this book and their coauthors in the published papers are given at the end of the book. It is a well-written and easy to read book and represents an up-to-date good source of information for students and researchers who want to learn and work in distribution theory.” – Miroslav M. Ristic, Professor, Department of Mathematics, University of Nis, Serbia


Publish with Nova Science Publishers

We publish over 800 titles annually by leading researchers from around the world. Submit a Book Proposal Now!