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Fat-tailed distributions. data, diagnostics and dependence / Volume 1 :
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 und...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London, England ; Hoboken, New Jersey :
ISTE : Wiley,
2014.
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| Colección: | Mathematics and statistics series (ISTE)
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.