Characterizations of Recently Introduced Univariate Continuous Distributions IV


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

Series: Mathematics Research Developments
BISAC: MAT029050; MAT029040; MAT027000

“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. These outstanding volumes prepared by Professor G.G. Hamedani are providing timely and most comprehensive mathematical/statistical tools for the First Step in applying and utilizing  continuous univariate distributions.” – Samad Hedayat, UIC Distinguished Professor Department of Mathematics, Statistics, and Computer Science University of Illinois, Chicago, Illinois, USA

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

“Our statistics training in the mid-1969s was largely based on Versatile Teachers  Lecture Notes and very few available  Classical Textbooks.  In  the area of Statistical  Distributions,  much later,  there came an Intellectual  Gift from the joint efforts of Johnson-Kotz-Kemp-Balakrishnan.  Several volumes were compiled and published in the Wiley Series. These are treasured collections in any statistical library.  In the same vein, this book by Hamedani will soon attract  attention of those of us who work in the areas of life distributions and reliability estimation in general. The author has put in tremendous intellectual efforts to come up with these compilations, and they undoubtedly serve as an Encyclopedia in this field of study.  They are amazing compilations of so many basic and derived (life) distributions and their characterizations. As we know, characterization problems are themselves very intriguing  and intellectually  challenging. The author has mastered the subject matter so much so that he has ventured into this difficult area in presenting a vast material with the utmost technical competence. On behalf of the researchers in this area of life distributions and allied topics, I congratulate the author. Simply told, this is a masterpieces in any sense of the term!” – Bikas K. Sinha, Professor of Statistics (Retired) Indian Statistical Institute,  Kolkata, India

“In  recent  years, numerous new probability  distributions have been developed for more sophisticated statistical modeling in challenging areas of new applications.  Advances in  statistical computing and the availability  of ever- increasing computing power have enabled us to fit highly complicated probability distributions in practice. The non-uniqueness of fitted distributions, however, raises the problem of determining the most appropriate distribution.  This is why characterizations of probability distributions distributions are of fundamental importance.  Hamedani has done a great service by collecting a huge number of characterizations in four volumes.  These extremely useful reference books are notable contributions to distribution  theory.” – Syed N.U. A. Kirmani,  Professor, Department of Mathematics, University of Northern Iowa, Iowa, USA

As mentioned in previous monographs (I, II & III), in designing a stochastic model for a particular modeling problem, an investigator will be vitally interested to know if their model fits the requirements of a specific underlying probability distribution. To this end, the investigator will rely on the characterizations of the selected distribution. Generally speaking, the problem of characterizing a distribution is an important problem in various fields and has recently attracted the attention of many researchers. Consequently, various characterization results have been reported in the literature. These characterizations have been established in many different directions. The present work deals with the characterization of a 800 newly proposed univariate continuous distributions as they became available to the author rather than the order of their importance. This work is a continuation of our previous works (Hamedani and Safavimanesh, 2017), (Hamedani, 2017), (Hamedani and Maadooliat, 2017), (Hamedani, 2018a), (Hamedani, 2018b), (Hamedani 2019) and (Hamedani 2021) on the characterizations of distributions introduced in 2019-2021. The current work and the previous published papers mentioned above may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.

Table of Contents

Chapter 1. Introduction

Chapter 2. Characterizations of Distributions


About the Author


Publish with Nova Science Publishers

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