A moment inequality for decreasing mean time to failure distributions with hypothesis testing application

Abstract

In this paper, we have derived a moment inequality for the Decreasing (Increasing) Mean Time to Failure (D(I)MTTF) life distributions. A new nonparametric test for testing exponentiality against DMTTF (IMTTF) alternatives is developed based on this moment inequality. Asymptotic property of the test statistic is derived under the null and alternative hypothesis. A comparative study has been carried out in terms of Pitman Asymptotic Relative Efficiency (PARE). The performance of the test is investigated by means of a simulation study. Utilizing the inverse probability censoring weighted scheme (IPCW) approach, we have also extended our test procedure to the case of right-censored data. Finally, application to real-life data sets has been carried out.

Keywords:

• Moment inequality
• U-statistics
• pitman's asymptotic relative efficiency
• right censoring
• inverse probability censoring weighted scheme

Acknowledgments

The authors thank the associate editor and the anonymous reviewer for their constructive suggestions which have resulted in an improved version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).