Statistical Analysis of Extreme Values

from Insurance, Finance, Hydrology and Other Fields

Author: Rolf-Dieter Reiss,Michael Thomas

Publisher: Birkhäuser

ISBN: 3034863365

Category: Mathematics

Page: 316

View: 415

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The statistical analysis of extreme data is important for various disciplines, including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical interference for extreme values. The entire text of this third edition has been thoroughly updated and rearranged to meet the new requirements. Additional sections and chapters, elaborated on more than 100 pages, are particularly concerned with topics like dependencies, the conditional analysis and the multivariate modeling of extreme data. Parts I–III about the basic extreme value methodology remain unchanged to some larger extent, yet notable are, e.g., the new sections about "An Overview of Reduced-Bias Estimation" (co-authored by M.I. Gomes), "The Spectral Decomposition Methodology", and "About Tail Independence" (co-authored by M. Frick), and the new chapter about "Extreme Value Statistics of Dependent Random Variables" (co-authored by H. Drees). Other new topics, e.g., a chapter about "Environmental Sciences", (co--authored by R.W. Katz), are collected within Parts IV–VI.

An Introduction to Statistical Modeling of Extreme Values

Author: Stuart Coles

Publisher: Springer Science & Business Media

ISBN: 1447136756

Category: Mathematics

Page: 209

View: 3883

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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.

Statistics of Extremes

Theory and Applications

Author: Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef Teugels

Publisher: John Wiley & Sons

ISBN: 0470012374

Category: Mathematics

Page: 522

View: 2592

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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.

Extreme Values

Statistical Analysis Using R

Author: Lee Fawcett,David Walshaw

Publisher: Wiley-Blackwell

ISBN: 9780470746455

Category: Computers

Page: 384

View: 7224

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The statistical analysis of extremes is becoming more and more prevalent as we observe increasing levels of variability and turbulence, both in the natural world, and within social organizations such as commercial and financial institutions. In this book, full coverage is given to the analysis of extreme value data using R, providing the reader with the best starting point for analyzing data when the aim is inference about extreme values of the underlying process. The main topics in extreme value analysis are featured, together with a clear practical guide on how to implement the relevant statistical analysis using R. The book is aimed at those needing to carry out extreme value analyses, examples used will be taken from applications in engineering, reliability studies and in financial analysis where extremes are of interest (e.g. insurance/reinsurance).

Extreme Value Theory

An Introduction

Author: Laurens de Haan,Ana Ferreira

Publisher: Springer Science & Business Media

ISBN: 0387239464

Category: Mathematics

Page: 418

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Focuses on theoretical results along with applications All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion Concentration is on the probabilistic and statistical aspects of extreme values Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity

An Introduction to Statistical Analysis of Random Arrays

Author: Vâčeslav Leonidovič Girko

Publisher: VSP

ISBN: 9789067642934

Category: Mathematics

Page: 673

View: 2725

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This book contains the results of 30 years of investigation by the author into the creation of a new theory on statistical analysis of observations, based on the principle of random arrays of random vectors and matrices of increasing dimensions. It describes limit phenomena of sequences of random observations, which occupy a central place in the theory of random matrices. This is the first book to explore statistical analysis of random arrays and provides the necessary tools for such analysis. This book is a natural generalization of multidimensional statistical analysis and aims to provide its readers with new, improved estimators of this analysis. The book consists of 14 chapters and opens with the theory of sample random matrices of fixed dimension, which allows to envelop not only the problems of multidimensional statistical analysis, but also some important problems of mechanics, physics and economics. The second chapter deals with all 50 known canonical equations of the new statistical analysis, which form the basis for finding new and improved statistical estimators. Chapters 3-5 contain detailed proof of the three main laws on the theory of sample random matrices. In chapters 6-10 detailed, strong proofs of the Circular and Elliptic Laws and their generalization are given. In chapters 11-13 the convergence rates of spectral functions are given for the practical application of new estimators and important questions on random matrix physics are considered. The final chapter contains 54 new statistical estimators, which generalize the main estimators of statistical analysis.

Statistical Analysis of Financial Data in R

Author: René Carmona

Publisher: Springer Science & Business Media

ISBN: 1461487889

Category: Business & Economics

Page: 588

View: 1870

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Although there are many books on mathematical finance, few deal with the statistical aspects of modern data analysis as applied to financial problems. This textbook fills this gap by addressing some of the most challenging issues facing financial engineers. It shows how sophisticated mathematics and modern statistical techniques can be used in the solutions of concrete financial problems. Concerns of risk management are addressed by the study of extreme values, the fitting of distributions with heavy tails, the computation of values at risk (VaR), and other measures of risk. Principal component analysis (PCA), smoothing, and regression techniques are applied to the construction of yield and forward curves. Time series analysis is applied to the study of temperature options and nonparametric estimation. Nonlinear filtering is applied to Monte Carlo simulations, option pricing and earnings prediction. This textbook is intended for undergraduate students majoring in financial engineering, or graduate students in a Master in finance or MBA program. It is sprinkled with practical examples using market data, and each chapter ends with exercises. Practical examples are solved in the R computing environment. They illustrate problems occurring in the commodity, energy and weather markets, as well as the fixed income, equity and credit markets. The examples, experiments and problem sets are based on the library Rsafd developed for the purpose of the text. The book should help quantitative analysts learn and implement advanced statistical concepts. Also, it will be valuable for researchers wishing to gain experience with financial data, implement and test mathematical theories, and address practical issues that are often ignored or underestimated in academic curricula. This is the new, fully-revised edition to the book Statistical Analysis of Financial Data in S-Plus. René Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering, and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over one hundred articles and eight books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and of the Society for Industrial and Applied Mathematics in 2010. He is on the editorial board of several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching statistics and research in signal analysis and financial engineering. He has worked for many years on energy, the commodity markets and more recently in environmental economics, and he is recognized as a leading researcher and expert in these areas.

Statistical Analysis of Management Data

Author: Hubert Gatignon

Publisher: Springer Science & Business Media

ISBN: 1402073151

Category: Business & Economics

Page: 334

View: 7260

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Statistical Analysis of Management Data is especially designed to provide doctoral students with a theoretical knowledge of the basic concepts underlying the most important multivariate techniques and with an overview of actual applications in various fields. The content herein addresses both the underlying mathematics and problems of application. As such, a reasonable level of competence in both statistics and mathematics is needed. This book is not intended as a first introduction to statistics and statistical analysis. Instead it assumes that the student is familiar with basic statistical techniques. The techniques are presented in a fundamental way but in a format accessible to students in a doctoral program, to practicing academicians, and to data analysts.

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Author: João Lita da Silva,Frederico Caeiro,Isabel Natario,Carlos Braumann

Publisher: Springer Science & Business Media

ISBN: 3642349048

Category: Mathematics

Page: 471

View: 9820

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This volume of the Selected Papers from Portugal is a product of the Seventeenth Congress of the Portuguese Statistical Society, held at the beautiful resort seaside city of Sesimbra, Portugal, from September 30 to October 3, 2009. It covers a broad scope of theoretical, methodological as well as application-oriented articles in domains such as: Linear Models and Regression, Survival Analysis, Extreme Value Theory, Statistics of Diffusions, Markov Processes and other Statistical Applications.

Statistical Analysis of Natural Disasters and Related Losses

Author: V.F. Pisarenko,M.V. Rodkin

Publisher: Springer Science & Business Media

ISBN: 3319014544

Category: Nature

Page: 81

View: 9246

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The study of disaster statistics and disaster occurrence is a complicated interdisciplinary field involving the interplay of new theoretical findings from several scientific fields like mathematics, physics, and computer science. Statistical studies on the mode of occurrence of natural disasters largely rely on fundamental findings in the statistics of rare events, which were derived in the 20th century. With regard to natural disasters, it is not so much the fact that the importance of this problem for mankind was recognized during the last third of the 20th century - the myths one encounters in ancient civilizations show that the problem of disasters has always been recognized - rather, it is the fact that mankind now possesses the necessary theoretical and practical tools to effectively study natural disasters, which in turn supports effective, major practical measures to minimize their impact. All the above factors have resulted in considerable progress in natural disaster research. Substantial accrued material on natural disasters and the use of advanced recording techniques have opened new doors for empirical analysis. However, despite the considerable progress made, the situation is still far from ideal. Sufficiently complete catalogs of events are still not available for many types of disasters, and the methodological and even terminological bases of research need to be further developed and standardized. The present monograph summarizes recent advances in the field of disaster statistics, primarily focusing on the occurrence of disasters that can be described by distributions with heavy tails. These disasters typically occur on a very broad range of scales, the rare greatest events being capable of causing losses comparable to the total losses of all smaller disasters of the same type. Audience: This SpringerBrief will be a valuable resource for those working in the fields of natural disaster research, risk assessment and loss mitigation at regional and federal governing bodies and in the insurance business, as well as for a broad range of readers interested in problems concerning natural disasters and their effects on human life.

Laws Of Small Numbers

Extremes And Rare Events

Author: Michael Falk,J]rg H]sler,Rolf-Dieter Reiss

Publisher: Springer Science & Business Media

ISBN: 9783764324162

Category: Mathematics

Page: 376

View: 6523

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Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages. Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.

Statistical Analysis of Stationary Time Series

Author: Ulf Grenander,Murray Rosenblatt

Publisher: American Mathematical Soc.

ISBN: 0821844377

Category: Mathematics

Page: 308

View: 3540

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From the Preface to the First Edition (1957): ``The purpose of this book is two-fold. It is written in the terminology of the theoretical statistician because one of our objectives is to direct his attention to an approach to time series analysis that is essentially different from most of the techniques used by time series analysts in the past. The second objective is to present a unified treatment of methods that are being used increasingly in the physical sciences and technology. We hope that the book will be of considerable interest to research workers in these fields. Keeping the first objective in mind, we have given a rigorous mathematical discussion of these new topics in time series analysis. The existing literature in time series analysis is characterized with few exceptions by a lack of precision both in conception and in the mathematical treatment of the problems dealt with. To avoid this vagueness, we have devoted more space to rigorous proofs than may appear necessary to some readers, but we believe that a study of the proofs will furnish valuable clues to the practical validity of the results and be an important guide to intuition. We have tried to balance the formal proofs with intuitive remarks and comments on practical applications. While the regularity assumptions we have required in many cases may seem restrictive, appropriately interpreted they give an indication of the range in which the methods are practically valid. We have made such interpretations in the comments accompanying the formal proofs.'' Readers should have knowledge of statistics and basic probability. The second edition was printed with corrections.

Statistical Analysis of Environmental Space-Time Processes

Author: Nhu D. Le,James V. Zidek

Publisher: Springer Science & Business Media

ISBN: 0387354298

Category: Science

Page: 342

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This book provides a broad introduction to the subject of environmental space-time processes, addressing the role of uncertainty. It covers a spectrum of technical matters from measurement to environmental epidemiology to risk assessment. It showcases non-stationary vector-valued processes, while treating stationarity as a special case. In particular, with members of their research group the authors developed within a hierarchical Bayesian framework, the new statistical approaches presented in the book for analyzing, modeling, and monitoring environmental spatio-temporal processes. Furthermore they indicate new directions for development.

Statistics of Extremes

Author: E. J. Gumbel

Publisher: Courier Corporation

ISBN: 0486154483

Category: Mathematics

Page: 400

View: 6783

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This classic text covers order statistics and their exceedances; exact distribution of extremes; the 1st asymptotic distribution; uses of the 1st, 2nd, and 3rd asymptotes; more. 1958 edition. Includes 44 tables and 97 graphs.

Advances in Financial Risk Management

Corporates, Intermediaries and Portfolios

Author: Jonathan A. Batten,Peter MacKay

Publisher: Springer

ISBN: 1137025093

Category: Business & Economics

Page: 411

View: 2097

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The latest research on measuring, managing and pricing financial risk. Three broad perspectives are considered: financial risk in non-financial corporations; in financial intermediaries such as banks; and finally within the context of a portfolio of securities of different credit quality and marketability.

Introduction to the Statistical Analysis of Categorical Data

Author: Erling B. Andersen

Publisher: Springer Science & Business Media

ISBN: 9783540623991

Category: Mathematics

Page: 265

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This book deals with the analysis of categorical data. Statistical models, especially log-linear models for contingency tables and logistic regression, are described and applied to real life data. Special emphasis is given to the use of graphical methods.

Statistical Analysis of Financial Data in S-Plus

Author: René Carmona

Publisher: Springer Science & Business Media

ISBN: 9780387202860

Category: Business & Economics

Page: 451

View: 3116

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This book develops the use of statistical data analysis in finance, and it uses the statistical software environment of S-PLUS as a vehicle for presenting practical implementations from financial engineering. It is divided into three parts. Part I, Exploratory Data Analysis, reviews the most commonly used methods of statistical data exploration. Its originality lies in the introduction of tools for the estimation and simulation of heavy tail distributions and copulas, the computation of measures of risk, and the principal component analysis of yield curves. Part II, Regression, introduces modern regression concepts with an emphasis on robustness and non-parametric techniques. The applications include the term structure of interest rates, the construction of commodity forward curves, and nonparametric alternatives to the Black Scholes option pricing paradigm. Part III, Time Series and State Space Models, is concerned with theories of time series and of state space models. Linear ARIMA models are applied to the analysis of weather derivatives, Kalman filtering is applied to public company earnings prediction, and nonlinear GARCH models and nonlinear filtering are applied to stochastic volatility models. The book is aimed at undergraduate students in financial engineering, master students in finance and MBA's, and to practitioners with financial data analysis concerns.

The New Statistical Analysis of Data

Author: T.W. Anderson,Jeremy Finn

Publisher: Springer Science & Business Media

ISBN: 9780387946191

Category: Mathematics

Page: 713

View: 7880

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A non-calculus based introduction for students studying statistics, business, engineering, health sciences, social sciences, and education. It presents a thorough coverage of statistical techniques and includes numerous examples largely drawn from actual research studies. Little mathematical background is required and explanations of important concepts are based on providing intuition using illustrative figures and numerical examples. The first part shows how statistical methods are used in diverse fields in answering important questions, while part two covers descriptive statistics and considers the organisation and summarisation of data. Parts three to five cover probability, statistical inference, and more advanced statistical techniques.