Moment inequality on new renewal better than used class of life distributions with hypothesis testing application

摘要

A moment inequality is derived for new renewal better (worse) than used NRBU (NRWU) distributions which demonstrate that if the mean life is finite, then all moments exist. Next a new test statistics for testing exponentiality against NRBU (NRWU) is introduced based on this inequality. It is shown that the proposed test is simple and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n=5(1)50. A set of real data is used as an example to elucidate the use of the proposed test statistics for practical reliability analysis.