On dynamic cumulative past inaccuracy measure based on extropy

Abstract

An alternate measure of extropy based on the cumulative distribution function rather than the probability density function of a random variable is called the cumulative past extropy (CPE). In this communication, the concept of CPE has been extended to cumulative past extropy inaccuracy (CPEI) and then to a dynamic version of it. A characterization problem for the proposed dynamic extropy inaccuracy measure has been studied under the proportional reversed hazard rate model. We also discuss the stochastic ordering of dynamic cumulative past extropy and certain results based on it. Some well-known lifetime distributions have been characterized using the proposed dynamic cumulative past extropy inaccuracy (DCPEI) measure. Three methods for nonparametric estimation of the DCPEI measure based on kernel and empirical estimators are proposed. Simulation results show that the kernel-based estimators of the DCPEI measure perform better than the empirical-based estimator under different sample sizes and times. A real data set is considered to show the behavior of the estimators in real cases.

Keywords:

• Cumulative past extropy
• reversed hazard rate
• mean past lifetime function
• reversed proportional hazard model
• inaccuracy

AMS 2000 Subject Classification:

• Primary 62N05
• Secondary 62F10

Acknowledgements

The authors thank the editor-in-chief, the associate editor, and the anonymous reviewers for their useful comments on the earlier version of this paper.