On the Operating Characteristics of Some Non-parametric Methodologies for the Classification of Distributions by Tail Behavior


Rick Ott
Mesa State College
Department of Computer Science, Mathematics, & Statistics

Abstract

        Classical extreme value theory partitions distributions into one of three categories based on the limiting behavior of the standardized maximum. These categories are commonly perceived as containing distributions of short, medium, and long tails respectively. Many have considered the classical medium class too abundant. The last 25 years have led to alternative methods of classifying distributions by tail behavior.

        This presentation will review the classical classification scheme along with a few of the alternative methods, specifically the density-quantile method of Parzen (1979), the hazard function refinements to the density-quantile approach by Schuster (1984), and the residual life function method by Rojo (1996). Refinements to one or more of these classification schemes will be presented. Tests to classify data as short-, medium-, or long-tailed by the definitions of Rojo will be presented.

This is joint work with Javier Rojo.