Quantile Inequalities for the Expectations of Generalized L-Statistics

Abstract

It is well known that if X_{r: n} and Y_{r: n} are order statistics from the i.i.d. samples with distribution functions F and G, respectively, such that F succeeds G in the convex order then . The result was extended to the generalized order statistics, and is also valid for their convex combinations. In this paper, we show that analogous relations hold true for much larger classes of linear combinations of generalized order statistics.

Keywords:

• Brunk inequality
• Convex order
• Generalized order statistics
• Jensen inequality
• Order statistics
• Steffensen–Jensen inequality

Mathematics Subject Classification:

• Primary 62G30
• Secondary 26A51
• 26D15