Fat-tailed distributions. Volume 1 : data, diagnostics and dependence / Roger M. Cooke, Daan Nieboer, Jolanta Misiewicz.

Format:

Book

Author/Creator:

Cooke, R. M. (Roger M.), author.

Nieboer, Daan, author.

Misiewicz, Jolanta, author.

Series:

Mathematics and statistics series (ISTE)

Mathematics and Statistics Series

Language:

English

Subjects (All):

Exchange traded funds.

Portfolio management.

Risk management.

Physical Description:

1 online resource (139 p.)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2014.

Language Note:

English

Summary:

This title 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 treat

Contents:

Cover; Title Page; Copyright; Contents; Introduction; 1: Fatness of Tail; 1.1. Fat tail heuristics; 1.2. History and data; 1.2.1. US flood insurance claims; 1.2.2. US crop loss; 1.2.3. US damages and fatalities from natural disasters; 1.2.4. US hospital discharge bills; 1.2.5. G-Econ data; 1.3. Diagnostics for heavy-tailed phenomena; 1.3.1. Historical averages; 1.3.2. Records; 1.3.3. Mean excess; 1.3.4. Sum convergence: self-similar or normal; 1.3.5. Estimating the tail index; 1.3.6. The obesity index; 1.4. Relation to reliability theory; 1.5. Conclusion and overview of the technical chapters

2: Order Statistics2.1. Distribution of order statistics; 2.2. Conditional distribution; 2.3. Representations for order statistics; 2.4. Functions of order statistics; 2.4.1. Partial sums; 2.4.2. Ratio between order statistics; 3: Records; 3.1. Standard record value processes; 3.2. Distribution of record values; 3.3. Record times and related statistics; 3.4. k-records; 4: Regularly Varying and Subexponential Distributions; 4.1. Classes of heavy-tailed distributions; 4.1.1. Regularly varying distribution functions; 4.1.2. Subexponential distribution functions

4.1.3. Related classes of heavy-tailed distributions4.2. Mean excess function; 4.2.1. Properties of the mean excess function; 5: Indices and Diagnostics of Tail Heaviness; 5.1. Self-similarity; 5.1.1. Distribution of the ratio between order statistics; 5.2. The ratio as index; 5.3. The obesity index; 5.3.1. Theory of majorization; 5.3.2. The obesity index of selected data sets; 6: Dependence; 6.1. Definition and main properties; 6.2. Isotropic distributions; 6.3. Pseudo-isotropic distributions

6.3.1. Covariation as a measure of dependence for essentially heavy-tail jointly pseudo-isotropic variables6.3.2. Codifference; 6.3.3. The linear regression model for essentially heavy-tail distribution; Conclusions and Perspectives; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed November 24, 2014).

ISBN:

1-119-05412-5

1-119-05420-6

1-119-05419-2

OCLC:

899001973