Title of the Book

Generalized Information Measures 
and Their Applications

Inder Jeet Taneja, Ph. D.
Departamento de Matemática
Universidade Federal de Santa Catarina
88.040-900 Florianópolis, SC, Brazil
Table of Contents Chapter 0
 

• Introduction

Chapter 1

• Shannon's Entropy

• Introduction
• Measures of Uncertainty: Shannon's Entropy
• Properties of Shannon's Entropy
• Multivariate Entropies
• Mutual Information
• Information Measures for Discrete Random Vectors
• Entropy Rate and Entropy Series
• Entropy Rate
• Entropy Series
• Entropy of a Continuous Random Variable
• Differential Entropy and Probability Distributions
• Entropy-Power Inequality

Chapter 2

• Information and Divergence Measures

• Introduction
• Relative Information and Inaccuracy
• Properties of Information Measures
• Distance Measures
• Divergence Measures
• Continuous Relative Information
• Minimum Relative Information Principle

Chapter 3

• Entropy-Type Measures

• Introduction
• Generalized Entropy Measures
• Entropies of Order r and Order (r,s)
• Entropy of Degree s and Degree (r,s)
• Entropy of kind t
• Entropies of Order 1 and Degree s and Order r and Degree s
• Unified (r,s)-Entropy
• Composition Relations Among the Unified (r,s)-Entropy Measures
• Properties of Unified (r,s)-Entropy
• Unified (r,s)-Entropy for Continuous Probability Distribuitions
• Characterizations of Generalized Entropies
• Entropy of Order r
• Entropy of Degree s
• Entropy of Degree (r,s)
• Entropy of Kind t
• Entropy of Order r and Degree s
• Important Observations
• Logic Among Eight Entropies
• List of Generalized Entropies
• Generalized Distance Measures

Chapter 4

• Generalized Information and Divergence Measures

• Generalized Information Measures
• Unified (r,s)-Relative Information
• Properties of Unified (r,s)-Relative Information
• Unified (r,s)-Inaccuracies
• Properties of Unified (r,s)-Inaccuracies
• Unified (r,s)-Divergence Measures
• First Generalizations
• Second Generalizations
• Properties of the Unified (r,s)-Divergence Measures

Chapter 5

• M-Dimensional Divergence Measures and Their Generalizations

• Introduction
• M-Dimensional Divergence Measures
• M-Dimensional Unified (r,s)-Divergence Measures
• M-Dimensional Unified (r,s)-Information Radii
• M-Dimensional Unified (r,s)-J-Divergences
• M-Dimensional Unified (r,s)-Arithmetic and Geometric Mean Divergences
• Composition Relations
• Properties of M-Dimensional Unified (r,s)-Divergence Measures

Chapter 6

• Unified (r,s)-Multivariate Entropies

• Introduction
• Different Forms of Unified (r,s)-Conditional Entropies
• Properties of Unified (r,s)-Conditional Entropies
• Biveriate Cases
• Multivariate Cases
• Unified (r,s)-Mutual Information
• Entropy of Degree s and its Multivariate Cases
• Conditional Entropies of Degree s
• Mutual Information of Degree s
• Properties of Conditional Entropies of degree s

Chapter 7

• Noiseless Coding and Generalized Information Measures

Chapter 8

• Channel Capacity and Source Coding Theorems

Chapter 9

• Statistical Aspects of Information Measures

Chapter 10

• Bayesian Probability of Error and Generalized Information Measures

Chapter 11

• Fuzzy Sets and Information Measures

Bibliography

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