Random Convex Combinations of m-Generalized Order Statistics

Abstract

The situation of identical distributions of a single m-generalized order statistic and a random convex combination of two neighboring m-generalized order statistics with beta-distributed weights is studied, and related characterizations of generalized Pareto distributions are shown.

Keywords:

• Characterizations
• Generalized order statistics
• Generalized Pareto distributions
• Random convex combination

Mathematics Subject Classification:

• 60E15
• 62G32

Acknowledgments

The results were established during the stay of the first author at the Institute of Statistics at the RWTH Aachen University, supported by a scholarship from DAAD (Deutscher Akademischer Austausch Dienst).

The authors are grateful to the referees for helpful comments and suggestions.