Characterizations of Aging Classes in Terms of Spacings Between Record Values

Abstract

Nonparametric classes of life distributions, such as the increasing likelihood ratio, increasing failure rate, decreasing mean residual life, new better than used, new better than used in the convex order, and new better than used in expectation classes as well as their duals, are characterized in terms of properties of the spacings between record values. A generalization of the usual record value sequence is needed.

Keywords:

• DMRL [IMRL]
• Hazard rate order
• IFR [DFR]
• ILR [DLR]
• Increasing convex order
• Likelihood ratio order
• NBU [NWU]
• NBUC [NWUC]
• NBUE [NWUE]
• Usual stochastic order

AMS Subject Classification:

• 60E15
• 60K10

ACKNOWLEDGMENTS

The authors would like to thank Professor Harry Joe for providing us his draft on this topic and his encouraging comments. This work was partially supported by National Natural Science Foundation of China (No.: 10771204), Program for New Century Excellent Talents in University (No.: NCET-04-0569), and FRG grant of Hong Kong Baptist University. The work was completed while the second author visited the Department of Mathematics, Hong Kong Baptist University, Hong Kong.