Statistics Of Extremes And Records In Random Sequences

Author : Satya N. Majumdar,Grégory Schehr
Publisher : Oxford University Press
Page : 257 pages
File Size : 41,6 Mb
Release : 2024-05-16
Category : Mathematics
ISBN : 9780192517883

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Statistics of Extremes and Records in Random Sequences by Satya N. Majumdar,Grégory Schehr Pdf

Rare events such as earthquakes, tsunamis, floods etc do not fortunately occur every day, but when they do, their effects are devastating. These days, such rare events are particularly important to understand to characterize the global warming and climate changes. In addition to natural catastrophes, rare events such as big financial crashes also play a significant role in economy. In the absence of predictive models, the best way forward is to analyse the statistics of these extreme events and draw conclusions from it about the probability of their occurrences. Extreme value statistics (EVS) and the statistics of records in a random sequence are examples of a truly interdisciplinary topic, spanning from statistics and mathematics on one side to physics of disordered systems on the other. They have tremendous importance and practical applications in a wide variety of fields, such as climate science, finance, spin-glasses, and random matrices. Statistics and mathematical literature have explored the subject of the classical theory of EVS. However, more recently, EVS started to play a very important role in statistical physics, in particular in disordered systems. This has led to a plethora of activities, both in the statistical physics and in the mathematics communities over the last few decades. This book develops the theory of rare events, both for the classical uncorrelated as well as for correlated sequences, in terms of simple models and examples. Statistics of Extremes and Records in Random Sequences is a pedagogical book with examples illustrating the basic tools and techniques that are essential to a student starting to work in this interesting and rapidly developing field.

Author : PROF SATYA N.. SCHEHR MAJUMDAR (PROF GREGORY.),Satya N. Majumdar,Grégory Schehr
Publisher : Oxford University Press
Page : 257 pages
File Size : 50,9 Mb
Release : 2024-06-20
Category : Mathematics
ISBN : 9780198797333

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Statistics of Extremes and Records in Random Sequences by PROF SATYA N.. SCHEHR MAJUMDAR (PROF GREGORY.),Satya N. Majumdar,Grégory Schehr Pdf

Rare events such as earthquakes, tsunamis, and floods fortunately do not occur every day, but when they do, their effects are devastating. Such rare events are particularly important in understanding and characterizing global warming and climate changes. In addition to natural catastrophes, rare events such as big financial crashes also play a significant role in the economy. In the absence of predictive models, the best way forward is to analyse the statistics of these extreme events and draw conclusions about the probability of their occurrences.Extreme value statistics (EVS) and the statistics of records in a random sequence are examples of a truly interdisciplinary topic, spanning from statistics and mathematics on one side to physics of disordered systems on the other. They have tremendous importance and practical applications in a wide variety of fields, such as climate science, finance, spin-glasses, and random matrices.Statistics and mathematical literature have explored the subject of the classical theory of EVS. However, more recently, EVS started to play a very important role in statistical physics, in particular in disordered systems. This has led to a plethora of activities, both in the statistical physics and in the mathematics communities over the last few decades. This book develops the theory of rare events, both for the classical uncorrelated as well as for correlated sequences, in terms of simple models and examples. Statistics of Extremes and Records in Random Sequences is a pedagogical book with examples illustrating the basic tools and techniques that are essential to a student starting to work in this interesting and rapidly developing field.

Author : M. R. Leadbetter,G. Lindgren,H. Rootzen
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461254492

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Extremes and Related Properties of Random Sequences and Processes by M. R. Leadbetter,G. Lindgren,H. Rootzen Pdf

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.

Author : Mohammad Ahsanullah
Publisher : Springer
Page : 137 pages
File Size : 53,7 Mb
Release : 2016-09-15
Category : Mathematics
ISBN : 9789462392229

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Extreme Value Distributions by Mohammad Ahsanullah Pdf

The aim of the book is to give a through account of the basic theory of extreme value distributions. The book cover a wide range of materials available to date. The central ideas and results of extreme value distributions are presented. The book rwill be useful o applied statisticians as well statisticians interrested to work in the area of extremen value distributions.vmonograph presents the central ideas and results of extreme value distributions.The monograph gives self-contained of theory and applications of extreme value distributions.

Author : Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas
Publisher : John Wiley & Sons
Page : 310 pages
File Size : 40,6 Mb
Release : 2020-03-31
Category : Mathematics
ISBN : 9781119721505

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Data Analysis and Applications 4 by Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas Pdf

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.

Author : Haroon M. Barakat,Osama M. Khaled,El-Sayed M. Nigm
Publisher : Cambridge Scholars Publishing
Page : 280 pages
File Size : 51,9 Mb
Release : 2019-05-14
Category : Mathematics
ISBN : 9781527534650

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Statistical Techniques for Modelling Extreme Value Data and Related Applications by Haroon M. Barakat,Osama M. Khaled,El-Sayed M. Nigm Pdf

This book tackles some modern trends and methods in the modelling of extreme data. Usually such data arise from random phenomena such as floods, hurricanes, air and water pollutants, extreme claim sizes, life spans, and maximum sizes of ecological populations. It provides the latest statistical methods to model these random phenomena to understand and predict them, thus allowing the avoidance of damage or at least minimizing it. In addition, this book sheds light on the mathematical and statistical theories on which applied modelling methods were built. Therefore, it has both an applied and theoretical orientation, and represents a valuable addition to existing literature on the modelling of extreme value data.

Author : Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 42,7 Mb
Release : 2004-10-15
Category : Mathematics
ISBN : 0471976474

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Statistics of Extremes by Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels Pdf

Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

Author : Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels
Publisher : John Wiley & Sons
Page : 522 pages
File Size : 47,8 Mb
Release : 2006-03-17
Category : Mathematics
ISBN : 9780470012376

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Statistics of Extremes by Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels Pdf

Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

Author : Jürg Hüsler,Rolf-Dieter Reiss
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236344

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Extreme Value Theory by Jürg Hüsler,Rolf-Dieter Reiss Pdf

The urgent need to describe and to solve certain problems connected to extreme phenomena in various areas of applications has been of decisive influence on the vital development of extreme value theory. After the pioneering work of M. Frechet (1927) and of R.A. Fisher and L.R.C. Tippett (1928), who discovered the limiting distributions of extremes, the importance of mathematical concepts of extreme behavior in applications was impressively demonstrated by statisticians like E.J. Gumbel and W. Weibull. The predominant role of applied aspects in that early period may be highlighted by the fact that two of the "Fisher-Tippett asymptotes" also carry the names of Gumbel and Weibull. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more of interest for mathematically oriented research workers. This was one of the reasons to organize a conference on extreme value theory which was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987.

Author : Pavle Mladenović
Publisher : Springer Nature
Page : 287 pages
File Size : 40,8 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9783031574122

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Extreme Values In Random Sequences by Pavle Mladenović Pdf

Author : Mohammad Ahsanullah
Publisher : Springer
Page : 125 pages
File Size : 44,7 Mb
Release : 2017-04-18
Category : Mathematics
ISBN : 9789462391390

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Characterizations of Univariate Continuous Distributions by Mohammad Ahsanullah Pdf

Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.

Author : Pavle Mladenović
Publisher : Springer
Page : 0 pages
File Size : 40,7 Mb
Release : 2024-06-04
Category : Mathematics
ISBN : 3031574117

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Extreme Values In Random Sequences by Pavle Mladenović Pdf

The main subject is the probabilistic extreme value theory. The purpose is to present recent results related to limiting distributions of maxima in incomplete samples from stationary sequences, and results related to extremal properties of different combinatorial configurations. The necessary contents related to regularly varying functions and basic results of extreme value theory are included in the first two chapters with examples, exercises and supplements. The motivation for consideration maxima in incomplete samples arises from the fact that real data are often incomplete. A sequence of observed random variables from a stationary sequence is also stationary only in very special cases. Hence, the results provided in the third chapter are also related to non-stationary sequences. The proof of theorems related to joint limiting distribution of maxima in complete and incomplete samples requires a non-trivial combination of combinatorics and point process theory. Chapter four provides results on the asymptotic behavior of the extremal characteristics of random permutations, the coupon collector's problem, the polynomial scheme, random trees and random forests, random partitions of finite sets, and the geometric properties of samples of random vectors. The topics presented here provide insight into the natural connections between probability theory and algebra, combinatorics, graph theory and combinatorial geometry. The contents of the book may be useful for graduate students and researchers who are interested in probabilistic extreme value theory and its applications.

Author : Tomasz Rychlik
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220947

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Projecting Statistical Functionals by Tomasz Rychlik Pdf

This book presents a method of establishing explicit solutions to classical problems of calculating the best lower and upper mean-variance bounds. The following families of distributions are taken into account: arbitrary, symmetric, symmetric unimodal, and U-shaped. The book is addressed to students, researchers, and practitioners in statistics and applied probability. Most of the results are recent, and a significant part of them has not been published yet. Numerous open problems are stated in the text.

Author : Anonim
Publisher : Unknown
Page : 240 pages
File Size : 40,7 Mb
Release : 1988
Category : Aeronautics
ISBN : MINN:30000005718410

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Scientific and Technical Aerospace Reports by Anonim Pdf

Author : Mohammad Ahsanullah
Publisher : University Press of America
Page : 326 pages
File Size : 42,8 Mb
Release : 2004
Category : Business & Economics
ISBN : 0761827943

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Record Values--theory and Applications by Mohammad Ahsanullah Pdf

In this book, Mohammad Ahsanullah provides a detailed description of the general theory and applications of record values. Professor Ahsanullah thoroughly discusses the most useful distributions and inferences based on record values, resulting in conclusions that are not available in previously published works.