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Extremes and Related Properties of Random Sequences and Processes

Extremes and Related Properties of Random Sequences and Processes
Author: M. R. Leadbetter
Publisher: Springer Science & Business Media
Total Pages: 344
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461254493

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Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.


Extremal and Related Properties of Stationary Processes. Part I. Extremes of Stationary Sequences

Extremal and Related Properties of Stationary Processes. Part I. Extremes of Stationary Sequences
Author: M. R. Leadbetter
Publisher:
Total Pages: 103
Release: 1979
Genre:
ISBN:

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This report considers the generalization of classical extreme value theory for independent random variables, to apply to stationary stochastic processes. Part 1 is concerned with stochastic sequences and part 2 will deal with continuous time processs. (Author).


Extreme Values, Regular Variation and Point Processes

Extreme Values, Regular Variation and Point Processes
Author: Sidney I. Resnick
Publisher: Springer
Total Pages: 334
Release: 2013-12-20
Genre: Mathematics
ISBN: 0387759530

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This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.


An Introduction to Statistical Modeling of Extreme Values

An Introduction to Statistical Modeling of Extreme Values
Author: Stuart Coles
Publisher: Springer Science & Business Media
Total Pages: 219
Release: 2013-11-27
Genre: Mathematics
ISBN: 1447136756

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Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.


Stationary Stochastic Processes

Stationary Stochastic Processes
Author: Georg Lindgren
Publisher: CRC Press
Total Pages: 378
Release: 2012-10-01
Genre: Mathematics
ISBN: 1466557796

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Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.


Probability Models for DNA Sequence Evolution

Probability Models for DNA Sequence Evolution
Author: Rick Durrett
Publisher: Springer Science & Business Media
Total Pages: 246
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475762852

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"What underlying forces are responsible for the observed patterns of variability, given a collection of DNA sequences?" In approaching this question a number of probability models are introduced and anyalyzed.Throughout the book, the theory is developed in close connection with data from more than 60 experimental studies that illustrate the use of these results.


Data Analysis and Applications 4

Data Analysis and Applications 4
Author: Andreas Makrides
Publisher: John Wiley & Sons
Total Pages: 310
Release: 2020-03-31
Genre: Mathematics
ISBN: 1119721504

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Data analysis as an area of importance has grown exponentially, especially during the past couple of decades. This can be attributed to a rapidly growing computer industry and the wide applicability of computational techniques, in conjunction with new advances of analytic tools. This being the case, the need for literature that addresses this is self-evident. New publications are appearing, covering the need for information from all fields of science and engineering, thanks to the universal relevance of data analysis and statistics packages. This book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis. The chapters included in this volume represent a cross-section of current concerns and research interests in these scientific areas. The material is divided into three parts: Financial Data Analysis and Methods, Statistics and Stochastic Data Analysis and Methods, and Demographic Methods and Data Analysis- providing the reader with both theoretical and applied information on data analysis methods, models and techniques and appropriate applications.


Asymptotic Methods in the Theory of Gaussian Processes and Fields

Asymptotic Methods in the Theory of Gaussian Processes and Fields
Author: Vladimir I. Piterbarg
Publisher: American Mathematical Soc.
Total Pages: 222
Release: 2012-03-28
Genre: Mathematics
ISBN: 0821883313

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This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.


Applied Extreme Value Statistics

Applied Extreme Value Statistics
Author: Arvid Naess
Publisher: Springer Nature
Total Pages: 277
Release:
Genre:
ISBN: 3031607694

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