Applications of Measure Theory to Statistics
Applications of Measure Theory to Statistics

Author: Gogi Pantsulaia

Publisher: Springer

Published: 2016-12-22

Total Pages: 147

ISBN-13: 3319455788

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This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics.

Entropy Measures, Maximum Entropy Principle and Emerging Applications
Entropy Measures, Maximum Entropy Principle and Emerging Applications

Author: Karmeshu

Publisher: Springer

Published: 2012-10-01

Total Pages: 300

ISBN-13: 3540362126

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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.

Conditional Measures and Applications
Conditional Measures and Applications

Author: M.M. Rao

Publisher: CRC Press

Published: 2005-05-25

Total Pages: 506

ISBN-13: 1420027433

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In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.M. Rao gave us the highly successful first edition of Conditional Measures and Applications. Until this groundbreaking work, conditional probability was relegated to scattered journal articles and

Computational Intelligence Techniques and Their Applications to Software Engineering Problems
Computational Intelligence Techniques and Their Applications to Software Engineering Problems

Author: Ankita Bansal

Publisher: CRC Press

Published: 2020-09-27

Total Pages: 620

ISBN-13: 100019194X

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Computational Intelligence Techniques and Their Applications to Software Engineering Problems focuses on computational intelligence approaches as applicable in varied areas of software engineering such as software requirement prioritization, cost estimation, reliability assessment, defect prediction, maintainability and quality prediction, size estimation, vulnerability prediction, test case selection and prioritization, and much more. The concepts of expert systems, case-based reasoning, fuzzy logic, genetic algorithms, swarm computing, and rough sets are introduced with their applications in software engineering. The field of knowledge discovery is explored using neural networks and data mining techniques by determining the underlying and hidden patterns in software data sets. Aimed at graduate students and researchers in computer science engineering, software engineering, information technology, this book: Covers various aspects of in-depth solutions of software engineering problems using computational intelligence techniques Discusses the latest evolutionary approaches to preliminary theory of different solve optimization problems under software engineering domain Covers heuristic as well as meta-heuristic algorithms designed to provide better and optimized solutions Illustrates applications including software requirement prioritization, software cost estimation, reliability assessment, software defect prediction, and more Highlights swarm intelligence-based optimization solutions for software testing and reliability problems

Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making
Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making

Author: Lilian Shi

Publisher: Infinite Study

Published:

Total Pages: 10

ISBN-13:

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The linguistic neutrosophic numbers (LNNs) can express the truth, indeterminacy, and falsity degrees independently by three linguistic variables. Hence, they are an effective tool for describing indeterminate linguistic information under linguistic decision-making environments. Similarity measures are usual tools in decision-making problems.

The Mathematical Theory of Communication
The Mathematical Theory of Communication

Author: Claude E Shannon

Publisher: University of Illinois Press

Published: 1998-09-01

Total Pages: 141

ISBN-13: 025209803X

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Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Several Trigonometric Hamming Similarity Measures of Rough Neutrosophic Sets and their Applications in Decision Making
Several Trigonometric Hamming Similarity Measures of Rough Neutrosophic Sets and their Applications in Decision Making

Author: KALYAN MONDAL

Publisher: Infinite Study

Published:

Total Pages: 11

ISBN-13:

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In 2014, Broumi et al. (S. Broumi, F. Smarandache, M. Dhar, Rough neutrosophic sets, Italian Journal of Pure and Applied Mathematics, 32 (2014), 493-502.) introduced the notion of rough neutrosophic set by combining neutrosophic sets and rough sets, which has been a mathematical tool to deal with problems involving indeterminacy and incompleteness. The real world is full of indeterminacy.

Mathematical Foundations and Applications of Graph Entropy
Mathematical Foundations and Applications of Graph Entropy

Author: Matthias Dehmer

Publisher: John Wiley & Sons

Published: 2017-09-12

Total Pages: 298

ISBN-13: 3527339094

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This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.

Random Measures, Theory and Applications
Random Measures, Theory and Applications

Author: Olav Kallenberg

Publisher: Springer

Published: 2017-04-12

Total Pages: 706

ISBN-13: 3319415980

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Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.

Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products
Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products

Author: Jiefeng Wang

Publisher: Infinite Study

Published:

Total Pages: 15

ISBN-13:

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A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments.