Record Values and Their Applications for Exponential and Rayleigh Distributions – A Handbook


Mohammad Ahsanullah – Professor Emeritus, Rider University, Lawrenceville, New Jersey, USA
Mohammad Shakil – Professor of Mathematics, Miami Dade College, Hialeah, Florida, USA

Series: Mathematics Research Developments
BISAC: MAT029000; SCI003000

Records arise naturally in many fields of study such as climatology, sports, science, engineering, medicine, traffic, and industry, among others. An observation is called a record if its value is greater than (or analogously, less than) all the preceding observations. The exponential and Rayleigh distribution play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of lifetime data. In this handbook, various properties of record values of univariate exponential and Rayleigh distributions, including most of the recent works, are reviewed. Some new results on mean residual life based on records and the minimum variance linear unbiased estimators of past records from univariate exponential distribution are presented.

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Table of Contents



Chapter 1. Record Values: Introduction

Chapter 2. Record Values of the Univariate Exponential Distribution

Chapter 3. Record Values of Rayleigh Distribution

Chapter 4. Characterization of Exponential Distribution Based on Record Values

Chapter 5. Characterizations of Rayleigh Distribution Based on Record Values

Chapter 6. Record Values of the Ratio of Two Exponential Random Variables

Chapter 7. Record Values of the Ratio of Two Rayleigh Random Variables

Chapter 8. Conclusion