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Author: M. Behara
Publisher: New Age International
ISBN:
Category : Coding theory
Languages : en
Pages : 296
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Book Description
A Unified Theory Of Measures Of Entropy Is Presented In This Research Monograph. After Covering Basic Materials On The Shannon And The Renyi Entropies, Which Are Additive Measures And Their Characterizations, The Monograph Focusses On Nonadditive Measures Of Entropy. Novel Techniques For The Systematic Discovery Of All Possible Entropy Measures Are Described. Geometric Entropies, Such As Parabolic Entropy, Are Derived From Geometric Configurations.When Subjected To Axioms Of Information Measures, On The Other Hand, Algebraic And Transcendental Functions Give Rise To Algebraic And Transcendental Entropies Respectively. Characterizations Of The Nonadditive Entropies Are Given By The Method Of Functional Equations While Properties Of All Entropies Are Studied In Detail. The Application Of Entropy In Coding Theory Is Extended To Parametric Entropies, Both Additive And Nonadditive, Because Of Their Superior Sensitivity Over The Shannon Entropy, A Nonparametric Measure.
Author: M. Behara
Publisher: New Age International
ISBN:
Category : Coding theory
Languages : en
Pages : 296
Get Book Here
Book Description
A Unified Theory Of Measures Of Entropy Is Presented In This Research Monograph. After Covering Basic Materials On The Shannon And The Renyi Entropies, Which Are Additive Measures And Their Characterizations, The Monograph Focusses On Nonadditive Measures Of Entropy. Novel Techniques For The Systematic Discovery Of All Possible Entropy Measures Are Described. Geometric Entropies, Such As Parabolic Entropy, Are Derived From Geometric Configurations.When Subjected To Axioms Of Information Measures, On The Other Hand, Algebraic And Transcendental Functions Give Rise To Algebraic And Transcendental Entropies Respectively. Characterizations Of The Nonadditive Entropies Are Given By The Method Of Functional Equations While Properties Of All Entropies Are Studied In Detail. The Application Of Entropy In Coding Theory Is Extended To Parametric Entropies, Both Additive And Nonadditive, Because Of Their Superior Sensitivity Over The Shannon Entropy, A Nonparametric Measure.
Author: Karmeshu
Publisher: Springer
ISBN: 3540362126
Category : Technology & Engineering
Languages : en
Pages : 300
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Book Description
The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.
Author: Vicenc Torra
Publisher: Springer
ISBN: 3319031554
Category : Technology & Engineering
Languages : en
Pages : 207
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Book Description
This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field.
Author: Jagat Narain Kapur
Publisher: John Wiley & Sons
ISBN: 9788122402162
Category : Technology & Engineering
Languages : en
Pages : 660
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Book Description
This Is The First Comprehensive Book About Maximum Entropy Principle And Its Applications To A Diversity Of Fields Like Statistical Mechanics, Thermo-Dynamics, Business, Economics, Insurance, Finance, Contingency Tables, Characterisation Of Probability Distributions (Univariate As Well As Multivariate, Discrete As Well As Continuous), Statistical Inference, Non-Linear Spectral Analysis Of Time Series, Pattern Recognition, Marketing And Elections, Operations Research And Reliability Theory, Image Processing, Computerised Tomography, Biology And Medicine. There Are Over 600 Specially Constructed Exercises And Extensive Historical And Bibliographical Notes At The End Of Each Chapter.The Book Should Be Of Interest To All Applied Mathematicians, Physicists, Statisticians, Economists, Engineers Of All Types, Business Scientists, Life Scientists, Medical Scientists, Radiologists And Operations Researchers Who Are Interested In Applying The Powerful Methodology Based On Maximum Entropy Principle In Their Respective Fields.
Author: Bruce Ebanks
Publisher: World Scientific
ISBN: 9814497878
Category : Mathematics
Languages : en
Pages : 293
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Book Description
How should information be measured? That is the motivating question for this book. The concept of information has become so pervasive that people regularly refer to the present era as the Information Age. Information takes many forms: oral, written, visual, electronic, mechanical, electromagnetic, etc. Many recent inventions deal with the storage, transmission, and retrieval of information. From a mathematical point of view, the most basic problem for the field of information theory is how to measure information. In this book we consider the question: What are the most desirable properties for a measure of information to possess? These properties are then used to determine explicitly the most “natural” (i.e. the most useful and appropriate) forms for measures of information.This important and timely book presents a theory which is now essentially complete. The first book of its kind since 1975, it will bring the reader up to the current state of knowledge in this field.
Author: Bruce Ebanks
Publisher: World Scientific
ISBN: 9789810230067
Category : Mathematics
Languages : en
Pages : 300
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Book Description
"This book is highly recommended for all those whose interests lie in the fields that deal with any kind of information measures. It will also find readers in the field of functional analysis..".Mathematical Reviews
Author: Roman S. Ingarden
Publisher: Springer Science & Business Media
ISBN: 9401718822
Category : Science
Languages : en
Pages : 317
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Book Description
This book has a long history of more than 20 years. The first attempt to write a monograph on information-theoretic approach to thermodynamics was done by one of the authors (RSI) in 1974 when he published, in the preprint form, two volumes of the book "Information Theory and Thermodynamics" concerning classical and quantum information theory, [153] (220 pp.), [154] (185 pp.). In spite of the encouraging remarks by some of the readers, the physical part of this book was never written except for the first chapter. Now this material is written completely anew and in much greater extent. A few years earlier, in 1970, second author of the present book, (AK), a doctoral student and collaborator of RSI in Toruli, published in Polish, also as a preprint, his habilitation dissertation "Information-theoretical decision scheme in quantum statistical mechanics" [196] (96 pp.). This small monograph presented his original results in the physical part of the theory developed in the Torun school. Unfortunately, this preprint was never published in English. The present book contains all these results in a much more modern and developed form.
Author: M. Behara
Publisher:
ISBN:
Category : Entropy
Languages : en
Pages : 41
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Book Description
Author: E. Pap
Publisher: Elsevier
ISBN: 0080533094
Category : Mathematics
Languages : en
Pages : 1633
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Book Description
The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Author: Leandro Pardo
Publisher: MDPI
ISBN: 3038979368
Category : Social Science
Languages : en
Pages : 344
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Book Description
This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly non-robust in cases of model misspecification under the presence of outlying observations. It is well-known that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.
