Engineering Analysis of Extreme Value Data: Selection of Models

Abstract

This paper discusses some of the existing statistical models for the analysis of extreme value data in the case of independence, pointing out their excellence and possible sources of error. Initially, the concept of order statistics is introduced, and the joint distribution of any set of order statistics is given. As simple examples, the distribution of the maximum, the minimum, any single order statistic, or any pair of order statistics are derived. Then, the problem of limit distribution is raised and carefully analyzed making a clear distinction between maxima and minima. It is shown that all models can be grouped in the Von Mises‐Jenkinson families, which include the three classical families. Several methods for selecting an adequate limit distribution based on data, including probability papers, least‐squares methods, and the curvature method are described. To clarify concepts, several illustrative examples of applications are included. Finally, a practical method for determining the limit distribution is described in detail.