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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.
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Ghosh et al. (2022) studied this question.
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