TRAN-STAT: statistics for environmental studies, No. 18, January 1982

Abstract

The statistical techniques that can be used for extreme value analysis of multivariate data are outlined. All the techniques suggested are derived from multivariate statistical procedures, ranging from classic discriminant analysis to modern cluster analysis algorithms. Also presented is an introduction to the Weibull or Fisher Type 3 Extreme Value distribution. This distribution is used in the study of reliability and in materials failure studies. The density and distribution functions are presented along with formulas for several estimable statistics. The Weibull distribution allows the option of including a third parameter, in addition to scale and shape parameters, which represents a threshold below which the probability of an effect or a measured response is zero. Simple parameter estimators are given, and it is noted that such estimators usually depend upon the logarithmic relationship between the Weibull and Extreme value distributions. The literature on parameter estimation is reviewed and papers are cited that propose unbiased and efficient estimators for parameter values, confidence intervals, and tolerance limits, and that can be used with censored samples. Finally, the use of life testing statistics for extreme value problems is discussed.