Extreme Value Distributions Theory and Applications 1st Edition by Samuel Kotz, Saralees Nadarajah ISBN 1860942245 9781860942242

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ISBN 10: 1860942245 
ISBN 13: 9781860942242
Author: Samuel Kotz, Saralees Nadarajah

This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions — one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field.

Extreme Value Distributions Theory and Applications 1st Table of contents:

Chapter 1 Univariate Extreme Value Distributions
1.1 Historical Survey
1.2 The Three Types of Extreme Value Distributions
1.3 Limiting Distributions and Domain of Attraction
1.4 Distribution Function and Moments of Type 1 Distribution
1.5 Order Statistics, Record Values and Characterizations
1.6 Generation, Tables, Probability Paper, Plots and Goodness of Fit
1.7 Methods of Inference
1.7.1 Moment Estimation
1.7.2 Simple Linear Estimation
1.7.3 Best Linear Unbiased (Invariant ) Estimation (BLUE)
1.7.4 Asymptotic Best Linear Unbiased Estimation
1.7.5 Maximum Likelihood Estimation
1.7.6 Method of Probability-Weighted Moments ( PWM)
1.7.7 Ranked Set Estimation
1.7.8 Conditional Method
1.7.9 Tolerance Limits
1.7.10 Minimum Distance Estimation of the Gumbel Distribution for Minima
1.8 Distributions Related to the Classical Extremal Distributions
1.8.1 Limiting Distributions of the rth Greatest (Least) Value
1.8.2 The Asymptotic Distribution of Range
1.8.3 Extremal Quotient
1.8.4 Log-Gamma Density
1.8.5 Smallest Extreme Value (SEV) Regression
1.9 Applications of the Classical Extreme Value Distributions
Chapter 2 Generalized Extreme Value Distributions
2.1 Basic Properties
2.2 Statistical Inference (Classical Approach)
2.3 Bayesian Inference
2.4 Robust Estimation
2.5 Zempleni’s Test of Hypothesis for the GEV Distribution
2.6 Estimation of Tail Index of a Distribution
2.7 Other Forms of Generalized Extreme Value Distributions
2.8 Some Selected Applications
Chapter 3 Multivariate Extreme Value Distributions
3.1 Limit Laws for Multivariate Extremes
3.2 Characterizations of the Domain of Attraction
3.2.1 Necessary Characterizations
3.2.2 Sufficient Characterizations
3.2.3 Necessary and Sufficient Characterizations
3.3 Characterizations of Multivariate Extreme Value Distributions
3.4 Parametric Families for Bivariate Extreme Value Distributions
3.4.1 Logistic Distributions (Tawn, 1988b)
3.4.2 Negative Logistic Distributions (Joe, 1990)
3.4.3 Bilogistic Distributions (Joe et al., 1992)
3.4.4 Negative Bilogistic Distributions (Coles and Tawn, 1994)
3.4.5 Gaussian Distributions (Smith, 1991)
3.4.6 Circular Distributions (Coles and Walshaw, 1994)
3.4.7 Beta Distributions (Coles and Tawn, 1991)
3.4.8 Polynomial Distributions (Nadarajah, 1999a)
3.4.9 Polynomial Distributions (Kluppelberg and May, 1999)
3.5 Parametric Families for Multivariate Extreme Value Distributions
3.5.1 Logistic Distributions (Tawn, 1990)
3.5.2 Two-Level Logistic Distributions (Tawn, 1990)
3.5.3 Negative Logistic Distributions (Joe, 1990)
3.5.4 Dirichlet Distributions (Coles and Tawn, 1991)
3.5.5 Time Series Logistic Distributions (Coles and Tawn, 1991)
3.5.6 Distributions Closed Under Margins
3.6 Statistical Estimation
3.6.1 Parametric Estimation
3.6.2 Semiparametric Estimation
3.6.3 Non-Parametric Estimation
3.7 Simulation
3.8 A Selective Survey of Applications of Multivariate Extreme Value Distributions
3.8.1 Some Earlier Applications
3.8.2 Directional Modelling of Wind Speeds
3.8.3 Applications to Structural Design

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Tags: Samuel Kotz, Saralees Nadarajah, Extreme