Laplace Transform-Based Nonparametric Test of Exponentiality against DMRL class with preservation under the Homogeneous Poisson Shock Model and applications in survival analysis and reliability.

This paper introduces a novel, computationally efficient nonparametric test for assessing the null hypothesis of exponentiality against alternatives belonging to the Decreasing Mean Residual Life (DMRL) class. The test statistic is developed using Laplace transform techniques in conjunction with the theory of U-statistics, ensuring asymptotic normality and scale invariance. In addition, we establish the preservation of the proposed methodology under the Homogeneous Poisson Shock Model, further extending its theoretical robustness in reliability contexts. Critical values are obtained through extensive Monte Carlo simulations under both complete and right-censored data, enhancing the method's practical applicability. A comprehensive simulation study demonstrates that the proposed test consistently outperforms classical procedures in terms of power across a wide range of alternative distributions commonly encountered in reliability and survival analysis. The usefulness of the method is further illustrated with real datasets, including COVID-19 mortality and clinical survival data, where the test successfully detects departures from exponentiality with DMRL characteristics. By combining advanced probabilistic transforms with nonparametric inference, this work provides a rigorous and scalable framework for lifetime data analysis, adaptable to the complex censoring mechanisms prevalent in medical and engineering applications.