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.
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.