Properties and estimation of the mean past lifetime

Abstract

Let T be a lifetime random variable. In order to study the properties of T in reliability theory and survival analysis, several measures are proposed in the literature. Among these measures, hazard rate, mean residual lifetime, reversed hazard rate and the mean past lifetime (MPL) play important roles. In the present paper, we focus mainly on the MPL. We investigate its properties in connection with other reliability measures. Some results on partial ordering and characterization are also given. Finally, we deal with its statistical estimation.

Keywords:

• mean past lifetime
• mean residual lifetime
• reversed hazard rate
• reliability
• characterizations
• partial ordering
• non-parametric estimation

AMS 2000 Subject Classification :

• Primary 62N05
• Secondary 62E10
• 62G05

Acknowledgements

Part of this research was performed while the first author was visiting the Université du Havre, France. The first author's research was supported by the Ordered and Spatial Data Center of Excellence of the Ferdowsi University of Mashhad, Iran.