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Extremes and Related Properties of Random Sequences and Processes
  • Language: en
  • Pages: 344

Extremes and Related Properties of Random Sequences and Processes

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.

Stationary Stochastic Processes for Scientists and Engineers
  • Language: en
  • Pages: 316

Stationary Stochastic Processes for Scientists and Engineers

  • Type: Book
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  • Published: 2013-10-11
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  • Publisher: CRC Press

Suitable for a one-semester course, this text teaches students how to use stochastic processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer. To enable hands-on practice, MATLAB code is available online.

Statistical Extremes and Applications
  • Language: en
  • Pages: 690

Statistical Extremes and Applications

The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards pro...

Dependence in Probability and Statistics
  • Language: en
  • Pages: 491

Dependence in Probability and Statistics

This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.

Statistical Inference
  • Language: en
  • Pages: 197

Statistical Inference

  • Type: Book
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  • Published: 2017-10-19
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  • Publisher: Routledge

Statistics is a subject with a vast field of application, involving problems which vary widely in their character and complexity.However, in tackling these, we use a relatively small core of central ideas and methods. This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the extraneous difficulties of complicatedmathematical manipulation.In order to compress the central body of ideas into a smallvolume, it is necessary to assume a fair degree of mathematicalsophistication on the part of the reader, and the book is intendedfor students of mathematics who are already accustomed tothinking in rather general terms about spaces and functions

Local Polynomial Modelling and Its Applications
  • Language: en
  • Pages: 358

Local Polynomial Modelling and Its Applications

  • Type: Book
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  • Published: 2018-05-02
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  • Publisher: Routledge

Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.

Markov Models & Optimization
  • Language: en
  • Pages: 316

Markov Models & Optimization

  • Type: Book
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  • Published: 2018-02-19
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  • Publisher: Routledge

This book presents a radically new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems. This approach is based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stochastic system models. A PDP is a Markov process that follows deterministic trajectories between random jumps, the latter occurring either spontaneously, in a Poisson-like fashion, or when the process hits the boundary of its state space. This formulation includes an enormous variety of applied problems in engineering, operations research, management science and economics as special cases; examples include queueing sy...

Sojourns And Extremes of Stochastic Processes
  • Language: en
  • Pages: 318

Sojourns And Extremes of Stochastic Processes

  • Type: Book
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  • Published: 2017-07-12
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  • Publisher: Routledge

Sojourns and Extremes of Stochastic Processes is a research monograph in the area of probability theory. During the past thirty years Berman has made many contributions to the theory of the extreme values and sojourn times of the sample functions of broad classes of stochastic processes. These processes arise in theoretical and applied models, and are presented here in a unified exposition.

Expansions and Asymptotics for Statistics
  • Language: en
  • Pages: 359

Expansions and Asymptotics for Statistics

  • Type: Book
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  • Published: 2010-05-07
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  • Publisher: CRC Press

Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti

Stability Problems for Stochastic Models
  • Language: en
  • Pages: 328

Stability Problems for Stochastic Models

  • Type: Book
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  • Published: 1994
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  • Publisher: VSP

Proceedings of the 11th International Seminar held in Sukhumi (Abkhazian Autonomous Republic) USSR, Sept., 1987. Ideas and methods used in stability theory of stochastic models. No index. Annotation copyrighted by Book News, Inc., Portland, OR