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Fat-tailed distributions : data, diagnostics and dependence / Roger M. Cooke, Daan Nieboer and Jolanta Misiewicz.

By: Contributor(s): Material type: TextTextSeries: Mathematics and statistics series, Mathematical models and methods in reliability set ; v 1.Publication details: London : ISTE Ltd, 2014.Description: x, 124 p. : illustrations ; 25 cmISBN:
  • 9781848217928
Subject(s): DDC classification:
  • 000SA.031 23 C773
Contents:
1. Fatness of tail -- 2. Order statistics -- 3. Records -- 4. Regularly varying and subexponential distributions -- 5. Indices and diagnostics of tail heaviness -- 6. Dependence -- Conclusions and perspectives -- Bibliography -- Index.
Summary: This book is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables.
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Includes bibliographical references and index.

1. Fatness of tail --
2. Order statistics --
3. Records --
4. Regularly varying and subexponential distributions --
5. Indices and diagnostics of tail heaviness --
6. Dependence --
Conclusions and perspectives --
Bibliography --
Index.

This book is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables.

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