Extreme Value Distributions: Theory and Applications
This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo 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. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."
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analysis applications approximation Balakrishnan Bayesian bivariate extreme value censored samples characterization coefficient Coles and Tawn convergence corresponding covariance defined denote density function dependence structure digamma function discussed distribution function domain of attraction efficient equation exponential distribution extreme value distribution extreme value theory flood GEV distribution given Gumbel distribution Haan joint density joint df limiting distribution linear unbiased estimators location parameter logistic distribution maxima maximum likelihood estimators method multivariate extreme value Nadarajah OBRE observations obtained order statistics Pareto distribution Pickands prior probability PWM estimators quantile random variables satisfy scale parameter sequence simulation standard tail threshold tolerance limits total independence transformation type 1 distribution type 1 extreme type 1 Gumbel unit Fréchet variance vector Weibull distribution