The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. This is an emerging area of study and research during the last two decades and is of potential interest in many fields. In this work the classical measures of uncertainty are sufficiently modified to meet the needs of lifetime data analysis. The book provides an exhaustive collection of materials in a single volume to make it a comprehensive source of reference.
The first treatise on the subject. It brings together the work that have appeared in journals on different disciplines. It will serve as a text for graduate students and practioners of special studies in information theory, as well as statistics and as a reference book for researchers. The book contains illustrative examples, tables and figures for clarifying the concepts and methodologies, the book is self-contained. It helps students to access information relevant to careers in industry, engineering, applied statistics, etc.
Author(s): S.M. Sunoj, G. Rajesh, N. Unnikrishnan Nair
Publisher: CRC Press/Science Publishers
Year: 2022
Language: English
Pages: 354
City: Boca Raton
Cover
Title Page
Copyright Page
Preface
Table of Contents
1. Preliminaries
1.1 Reliability analysis and information theory
1.2 Basic reliability functions
1.3 Quantile-based reliability functions
1.4 Quantile function models
1.5 Ageing and associated criteria
1.6 Concepts based on hazard rate
1.7 Concepts based on residual life
1.8 Classes based on survival function
1.9 Concepts in reversed time
1.10 Order statistics
1.11 Log concave and convex distributions
1.12 Weighted distributions
1.13 Stochastic orders
2. Residual Entropy
2.1 Introduction
2.2 Definition and properties of entropy
2.3 Differential entropy
2.4 Residual entropy
2.5 Order statistics
2.6 Quantile-based residual entropy
2.7 Weighted residual entropy
2.8 Stochastic orders
2.9 Estimation and testing
2.10 Residual extropy
3. Entropy of Past Life
3.1 Past entropy
3.2 Properties of past entropy
3.3 Past quantile entropy
3.4 Order statistics
3.5 Weighted past entropy
3.6 Interval entropy
3.7 Past extropy
4. Generalized Entropies
4.1 Introduction
4.2 Renyi entropy
4.3 Tsallis entropy
4.4 Varma entropy
4.5 Other entropies
5. Divergence Measures
5.1 Introduction
5.2 Kullback-Leibler divergence
5.3 Renyi’s divergence
5.4 Varma divergence
5.5 Csiszar’s family
5.6 Chernoff distance
5.7 Lin-Wong divergence
6. Inaccuracy
6.1 Introduction
6.2 Inaccuracy of residual lives
6.3 Quantile-based inaccuracy
6.4 Past inaccuracy measure
6.5 Estimation
7. Cumulative Entropy
7.1 Introduction
7.2 Cumulative entropy of residual life
7.3 Cumulative residual entropy of order n
7.4 Dynamic version of Cn
7.5 Weighted cumulative residual entropy
7.6 Cumulative entropy
7.7 Quantile-based cumulative entropy
7.8 Other topics
8. Generalized Cumulative Entropy and Divergence
8.1 Introduction
8.2 Survival and failure entropies
8.3 Cumulative divergence
8.4 Cumulative Tsallis entropy
8.5 Cumulative Varma’s entropy
8.6 Cumulative residual inaccuracy
8.7 Generalized cumulative residual entropy
References
Index
