A Distributional Identity for Generalized Order Statistics with Characterizations Useful for Prediction

Mathematical Methods of Statistics, vol. 34, pp. 240–250

Abstract

A distributional identity for generalized order statistics is presented in two versions along with a characterization of exponential and Pareto distributions, respectively, under mild conditions. In its multiplicative form, the identity extends previous random dilation results in models of ordered random variables. The relations can be utilized as a statistical method to predict future generalized order statistics or other quantities of interest within submodels.

Authors 4

1. Mahdi Alimohammadi corresponding

   Alzahra University

   Affiliation as printed

   Department of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

2. Udo Kamps Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, Germany

   Institute of Statistics, RWTH Aachen University, D-52056, Aachen, Germany

3. Fariba Azizi

   Alzahra University

   Affiliation as printed

   Department of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

4. Marziyeh Pourbagher

   Alzahra University

   Affiliation as printed

   Department of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran