Inequalities for generalized order statistics from some restricted family of distributions

Abstract

The Steffensen inequality is applied to derive quantile bounds for the expectations of generalized order statistics from a distribution belonging to a particular subclass of distributions. The subclass consists of F having the property that F⁻¹(0+)=x₀>0 and that x →[1− F(x)]x^z is nonincreasing for all x > X₀ and some z > 0.

Keywords:

• order statistics
• record statistics
• Steffensen inequality
• Pareto distribution

Additional information

Notes on contributors

L. Gajek