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Laws of Small Numbers: Extremes and Rare Events


Laws of Small Numbers: Extremes and Rare Events


3rd ed. 2010

von: Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss

CHF 142.00

Verlag: Birkhäuser
Format: PDF
Veröffentl.: 07.10.2010
ISBN/EAN: 9783034800099
Sprache: englisch
Anzahl Seiten: 509

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

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. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation.

Reviews of the 2nd edition:

"In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field."
David Stirzaker, Bulletin of the London Mathematical Society

"Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook."
Holger Drees, Metrika
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. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation.

Reviews of the 2nd edition:

"In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field."
David Stirzaker, Bulletin of the London Mathematical Society

"Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook."
Holger Drees, Metrika
Preface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- Part I. The IID Case: Functional Laws Of Small Numbers.- 1 Functional Laws of Small Numbers.- 2 Extreme Value Theory.- 3 Estimation of Conditional Curves.- Part II. The IID Case: Multivariate Extremes.- 4 Basic Theory of Multivariate Maxima.- 5 Multivariate Generalized Pareto Distributions.- 6 The Pickands Approach in the Bivariate Case.- 7 Multivariate Extremes: Supplementary Concepts and Results.- Part III. Non-IID Observations.- 8 Introduction to the Non-IID Case.- 9 Extremes of Random Sequences.- 10 Extremes of Gaussian Processes.- 11 Extensions for Rare Events.- 12 Statistics of Extremes.- Author Index.- Subject Index.- Bibliography.
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. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation.

Reviews of the 2nd edition:
"In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field."
David Stirzaker, Bulletin of the London Mathematical Society

"Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook."
Holger Drees, Metrika
<p>Third edition of the successful seminar book, with special consideration of the recent change of focus of extreme value theory Focus on large observations defined as exceedances over high thresholds Emphasis on multivariate generalized Pareto distributions</p><p>Includes supplementary material: sn.pub/extras</p>
<p>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. </p><p>Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory.</p><p>This book is accessible to graduate students and researchers with basic knowledge in probability theory and, partly, in point processes and Gaussian processes. The required statistical prerequisites are minimal.</p>

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