Distances between models of generalized order statistics

Abstract

The concept of generalized order statistics is a distribution theoretical set-up, which contains a variety of models for ordered data as particular cases, such as common order statistics, sequential order statistics, progressively type-II censored order statistics, record values, kth record values, and Pfeifer record values. In order to quantify the structure of generalized order statistics, distances between different respective models are measured by means of explicit expressions for divergences and distances applied to joint densities of ordered random variables. The results are exemplarily utilized to find a closest common order statistics model to some given model of sequential order statistics. Moreover, statistical applications in reliability are shown.