Extreme value theory in engineering / Enrique Castillo.

This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent advances. A collection of 150 examples illustrates the theoretical results and takes the reader from...

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Bibliographic Details
Main Author: Castillo, Enrique, 1946-
Format: eBook
Published: Boston : Academic Press, ©1988.
Series:Statistical modeling and decision science.
Online Access:Click for online access
Table of Contents:
  • Front Cover; Extreme Value Theory in Engineering; Copyright Page; Table of Contents; Preface; Part I: Introduction; Chapter 1. Introduction and Motivation; 1.1. Introduction; 1.2. Some Engineering Examples Where Extreme Value Theory Is of Significance; 1.3. New Developments in Extreme Value Theory; 1.4. Aim of the Book; 1.5. Organization of the Book; 1.6. Some Classical Statistical Concepts; Part II: Order Statistics; Chapter 2. Order Statistics; 2.1. Introduction; 2.2. Concept of Order Statistic; 2.3. Order Statistics from Independent and Identically Distributed Samples.
  • 2.4. Order Statistics from Dependent SamplesPart III: Asymptotic Distribution of Sequences of Independent Random Variables; Chapter 3. Asymptotic Distributions of Maxima and Minima (I.I.D. Case); 3.1. Introduction and Motivation; 3.2. Statement of the Problem; 3.3. Limit Distributions and Domains of Attraction; 3.4. Von-Mises Forms; 3.5. Normalizing Constants; 3.6. Domain of Attraction of a Given Distribution; 3.7. Asymptotic Joint Distribution of Maxima and Minima; 3.8. Asymptotic Distributions of Range and Midrange; 3.9. Asymptotic Distributions of Maxima of Samples with Random Size.
  • 3.10. Approximation of Distribution Functions in Their Tails3.11. The Penultimate Form of Approximation to Extremes; Chapter 4. Shortcut Procedures: Probability Papers and Least-Squares Methods; 4.1. Introduction; 4.2. The Theoretical Bases of Probability Paper; 4.3. The Problem of Plotting Positions; 4.4. Acceptance Regions; 4.5. Some Recommendations for the Use of Probability Papers in Extreme Value Problems; 4.6. Weighted Least-Squares Methods; Chapter 5. The Gumbel, Weibull and Frechet Distributions; 5.1. Introduction; 5.2. The Gumbel Distribution; 5.3. The Weibull Distribution.
  • 5.4. The Frechet DistributionChapter 6. Selection of Limit Distributions from Data; 6.1. Statement of the Problem; 6.2. Methods for Determining the Domain of Attraction of a Parent Distribution from Samples; Chapter 7. Limit Distributions of k-th order Statistics; 7.1. Introduction; 7.2. Statement of the Problem and Previous Definitions; 7.3. Limit Distributions of Upper and Lower Order Statistics; 7.4. Limit Distributions of Other Order Statistics; 7.5. Asymptotic Distributions of k-th Order Statistics of Samples with Random Sizes.
  • Part IV: Asymptotic Distribution of Sequences of Dependent Random VariablesChapter 8. Limit Distributions in the Case of Dependence; 8.1. Introduction; 8.2. Exchangeable Variables; 8.3. Dependence Conditions; 8.4. Limit Distributions of Maxima and Minima; 8.5. Asymptotic Distributions of k-th Extremes; Part V: Multivariate Case; Chapter 9. Multivariate and Regression Models Related to Extremes; 9.1. Introduction; 9.2. Regression Models; 9.3. Bivariate Models with Weibull Conditionals; Chapter 10. Multivariate Extremes; 10.1. Introduction; 10.2. Dependence Functions; 10.3. Limit Distributions.