General bounds and inequalities in order statistics

Abstract

This article is primarily a review of recent work on inequalities requiring no or only mild ssumptions.As feature,unified approaches are given for the derivation of algebraic inequalities involving linear functions of order statistics. Various inequalities for the expected value of such functions are presented. A new result is that a class of these inequalities can be improved by use of a theorem for ordered sums. Some other recent results are noted. Applications are indicated throughout.

Keywords:

• Cauchy's inequality
• convexity
• Schurconcavity
• jenen's inequality
• order sums
• studentized statstics