Abstract
In the spirit of [J. Statist. Planning Inf. 92 (2001) 121], a moment inequality for the class of new better than used failure rate NBUFR (NWUFR) of aging distributions is derived. From this inequality we constructed a new family of test statistics. We used this family in testing exponentiality against NBUFR (NWUFR). The asymptotic normality of the proposed statistic is presented. Pitman asymptotic efficacy, the power and critical values of the proposed statistic are calculated. It is shown that, the proposed statistic has a high asymptotic relative efficiency with respect to tests of other classes for commonly used alternatives.
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