EMS Tracts in Mathematics Vol. 5
ISBN 978-3-03719-045-6
April 2008, 268 pages, hardcover, 17 x 24 cm.
This book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables.
In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group X. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac?Bernstein, Skitovich?Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of X. Group analogs of the Cramer and Marcinkiewicz theorems are also studied.
The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory.
ISBN: 978-0-470-03554-2
Hardcover
1144 pages
September 2008
Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years have witnessed a renewed and expanding interest in the topic as it begins to play a key role in bioinformatics, e-commerce, machine learning, security, data mining and wireless mobile computing when it comes to the issues of effectiveness, robustness and uncertainty.
The Handbook of Granular Computing offers a comprehensive reference source for the granular computing community, edited by and with contributions from leading experts in the field.
Includes chapters covering the foundations of granular computing, interval analysis and fuzzy set theory; hybrid methods and models of granular computing; and applications and case studies.
Divided into 5 sections: Preliminaries, Fundamentals, Methodology and Algorithms, Development of Hybrid Models and Applications and Case Studies.
Presents the flow of ideas in a systematic, well-organized manner, starting with the concepts and motivation and proceeding to detailed design that materializes in specific algorithms, applications and case studies.
Provides the reader with a self-contained reference that includes all pre-requisite knowledge, augmented with step-by-step explanations of more advanced concepts.
The Handbook of Granular Computing represents a significant and valuable contribution to the literature and will appeal to a broad audience including researchers, students and practitioners in the fields of Computational Intelligence, pattern recognition, fuzzy sets and neural networks, system modelling, operations research and bioinformatics.
(Wiley sereis in probability and statistics)
ISBN: 978-0-470-07371-1
Hardcover
424 pages
July 2008
This book provides a unified treatment of the use of mixed models for analyzing correlated data. Models for non-normal data, i.e. binary or count data, and generalized linear and nonlinear models are described and illustrated. The first few chapters of the book introduce all the major ideas in a context that will be familiar to most students of statistics. This text provides an accessible treatment of many of the newer statistical models for correlated, non-normally distributed data. The book's unified treatment addresses the needs of applications-oriented users of statistical packages and also graduate students in statistics.
ISBN: 978-0-470-03549-8
Hardcover
1922 pages
September 2008
Leading the way in this field, the Encyclopedia of Quantitative Risk Analysis and Assessment will be the first publication to offer a modern, comprehensive and in-depth resource to the huge variety of disciplines involved.
A truly international work, its coverage ranges across risk issues pertinent to life scientists, engineers, policy makers, healthcare professionals, the finance industry, the military and practising statisticians.
Wiley is now pleased to announce this landmark reference work publishing in July 2008. Drawing on the expertise of world-renowned authors and editors in this field this title will provide up-to-date material on drug safety, investment theory, public policy applications, transportation safety, public perception of risk, epidemiological risk, national defence and security, critical infrastructure, and program management.
This major publication is easily accessible for all those involved in the field of risk assessment and analysis. For ease-of-use it will be available in print and online.
Risk Management Financial/Credit Risk Computer Security Reliability -
Mathematical and Statistical methods Reliability -
Management Science Bayesian/Decision Theory Environmental Risk Clinical Risk Public Health/Epidemiology of Risk Toxic Substances/Chemical Risk Insurance/Actuarial Risk Homeland Security
ISBN: 978-0-470-23286-6
Hardcover
480 pages
July 2008
This book provides the development of the theoretical concepts and computational techniques of linear programming and game theory and explores applications of these topics in the social, life, and managerial sciences. The Third Edition features various additions and improvements that have been developed over the last decade, most significantly the integration of new computer software, LP Assistant, to assist the reader in learning and using the simplex algorithm, and the spreadsheet tool Solver to solve linear, non-linear, and integer programming problems.