Characterizations by Power Contractions of Order Statistics

Abstract

Some general procedures are obtained to characterize the distribution of a sample of independent and identically distributed random variables by power contractions of the associated order statistics. Some necessary conditions for these kinds of relations are given, including some ordering properties. The results can also be applied to the family of distributions defined by Jones (2004, Test 13, 1–43). The general results are illustrated by obtaining known and new characterizations of some probability models.

Keywords:

• Characterization
• Order statistics
• Power contractions

Mathematics Subject Classification:

• Primary 62E10
• Secondary 62G30

Acknowledgments

I wish to thank Professor Barry Arnold and the anonymous referees for several helpful comments. This work is partially supported by Ministerio de Ciencia y Tecnología under grant MTM2006-12834 and Fundación Séneca (CARM) under grant 00698/PI/04.