Projection Mean–Variance Bounds on Expectations of kth Record Values from Restricted Families

Abstract

We present sharp mean–variance bounds for expectations of kth record values based on distributions coming from restricted families of distributions. These families are defined in terms of convex or star ordering with respect to generalized Pareto distribution. The bounds for expectations of kth record values from DD, DFR, DDA, and DFRA families are special cases of our results. The bounds are derived by application of the projection method.

Keywords:

• Convex order
• Generalized failure rate function
• Generalized Pareto distribution
• kth record values
• Projection method
• Star order

Mathematics Subject Classification:

• 60G30

Acknowledgment

The author is very grateful to referees for many useful comments and suggestions.