Moment Inequalities for Discrete Ageing Families

Abstract

Some moment inequalities are well known in the literature to be valid for several continuous ageing families. In this article, we establish moment inequalities for D-ILR [D-DLR], DS-IFR, DS-DMRL [DS-IMRL], DW-NBU [DS-NWU], DW-NBUE [DS-NBUE] and DW-HNBUE [DS-HNWUE] families of discrete non-negative integer-valued random variables, and also give some minor results about moment inequalities of random variables that are ordered in the mean residual life order.

Keywords:

• Moment inequalities
• Ageing
• Log-concave
• Log-convex
• Stochastic orders
• D-ILR [D-DLR]
• DS-IFR
• DS-DMRL [DS-IMRL]
• DW-NBU [DS-NWU]
• DW-NBUE [DS-NWUE]
• DW-HNBUE [DS-HNWUE].

Acknowledgments

The first author was supported by the Natural Science Foundation of China (Grant No.: 10171093) and the National 973 Fundamental Research Program on Financial Engineering (Grant No.: G1998030418). The third author acknowledges the financial assistance obtained from CSIR vide sanctioned No. 25(0125)/02/EMR-II dt. 30.5.2002. The authors are very grateful to the referee for his valuable comments.