On study of dynamic survival and cumulative past entropies

Abstract

Recently, a new class of measure of uncertainty, called “dynamic survival entropy”, has been defined and studied in the literature. Based on this entropy, DSE(α) ordering, IDSE(α), and DDSE(α) classes of life distributions are defined and some results are studied. In this paper, our main aim is to prove some more results of the ordering and the aging classes of life distributions mentioned above. Some important distributions such as exponential, Pareto, Pareto II, and finite range distributions are also characterized. Here we have defined cumulative past entropy and proved some interesting results.

Keywords:

• Failure rate function
• Reversed hazard rate function
• Mean residual life function
• Minimal repair
• Stochastic orders

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60E15
• 60K10

Acknowledgments

The authors are thankful to the editor and the referee for their valuable comments and suggestions on an earlier draft of the manuscript. The financial support (Vide No. 2/48(13)/2011/-R&D II/3246 dated 21.03.2012) from NBHM is acknowledged with thanks by Amarjit Kundu.