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Stein's method and applications
Authors: --- --- ---
ISBN: 1281880795 9786611880798 9812567674 9789812567673 9789812562814 9812562818 9781281880796 6611880798 Year: 2005 Publisher: Singapore : New Jersey ; Hong Kong : Singapore University Press ; World Scientific,

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Abstract

Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 2003, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers i


Book
Riesz Probability Distributions
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ISBN: 9783110713374 3110713373 Year: 2021 Publisher: Berlin Boston

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This book is a useful overview of results in multivariate probability distributions and multivariate analysis as well as a reference to harmonic analysis on symmetric cones adapted to the needs of researchers in analysis and probability theory.


Book
Multivariate Characteristic and Correlation Functions.
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ISSN: 01790986 ISBN: 3110223996 9783110223996 9783110223989 3110223988 Year: 2013 Volume: 50 Publisher: Berlin De Gruyter

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In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.


Book
Gibbs measures on Cayley trees
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ISBN: 9814513385 9789814513388 9789814513371 9814513377 Year: 2013 Publisher: [Hackensack] New Jersey

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The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Mor


Book
The theory of probability
Author:
ISBN: 0828401322 Year: 1968 Publisher: New York Chelsea

One-dimensional stable distributions
Authors: --- ---
ISBN: 0821845195 9780821845196 Year: 1986 Volume: 65 Publisher: Providence (R.I.): American Mathematical Society

Regional frequency analysis : an approach based on L-moments
Authors: ---
ISBN: 0521430453 9780521430456 9780511529443 9780521019408 Year: 1997 Publisher: Cambridge ; New York Cambridge University Press

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Abstract

Extreme environmental events, such as floods, droughts, rainstorms, and high winds, have severe consequences for human society. How frequently an event of a given magnitude may be expected to occur is of great importance. Planning for weather-related emergencies, design of civil engineering structures, reservoir management, pollution control, and insurance risk calculations, all rely on knowledge of the frequency of these extreme events. Estimation of these frequencies is difficult because extreme events are by definition rare and the data record is often short. Regional frequency analysis resolves this problem by "trading space for time"; data from several sites are used in estimating event frequencies at any one site. L-moments are a recent development within statistics. They form the basis of an elegant mathematical theory in their own right and can be used to facilitate the estimation process in regional frequency analysis. L-moments methods are demonstrably superior to those that have been used previously and are now being adopted by many organizations worldwide. This book is the first complete account of the L-moment approach to regional frequency analysis. It brings together results that previously were scattered among academic journals and also includes much new material. Regional Frequency Analysis comprehensively describes the theoretical background to the subject, is rich in practical advice for users, and contains detailed examples that illustrate the approach. This book will be of great value to hydrologists, atmospheric scientists, and civil engineers concerned with environmental extremes.

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