A Quantile-Based Approach for Testing Exponentiality Against DMTTF Alternatives

In this article, we introduce a family of nonparameteric tests for exponentiality against alternatives from the decreasing mean time to failure family, employing the quantile-based formulation of the mean time to failure function. We derive the exact null distribution for the proposed family of test statistics and establish their consistency and asymptotic normality. To evaluate the performance of the test, we compare it with existing tests through Monte Carlo simulations. Finally, we utilize real-world data to illustrate the implementation of our test.