Extreme‐Value Distributions

Abstract

This is an expository survey of the (univariate) theory of extreme values and the estimation of the parameters of the related extremevalue distributions. This survey was written at the invitation of Professors N.L. Johnson and S. Kotz, editors of the forthcoming Encyclopedia of Statiatical Seneee'to be published by John Wiley and Sons, Inc., New York. The theory of extreme values plays a fundamental role in several areas of applied statistics, such as the analysis of flood flows, the reliability of complex systems, the analysis of air pollution data, etc. In addition to surveying (without proofs) the basic results of extreme value theory and the estimators of the parameters of the extreme value distributions, this survey presents a brief discussion of the current research in these areas. The theory of extreme values, and the extreme value distributions, play an important role in theoretical and applied statistics. For example, extreme value distributions arise quite naturally in the study of size effect on material strengths, the occurrence of floods and droughts, the reliability of systems made up of a large number of