Non-Parametric Hypothesis Testing for Used Better than Aged in Laplace Transform (UBAL) Life Distributions: A Moment Inequalities Approach with Medical Applications

Life distribution comparison is important in reliability and survival analysis to model system aging and longevity. The article develops a non-parametric hypothesis test procedure for testing exponentiality against the Used Better than Aged in Laplace transform (UBAL) family of life distributions. The test in this case is developed based on moment inequalities in the Laplace transform, which yields a computationally straightforward and theoretically sound methodology. We establish the asymptotic behavior of the test statistic and evaluate its performance through Monte Carlo simulations, showing acceptable power against common alternatives such as the Weibull, linear failure rate, and Makeham distributions. Critical values are also provided for practical use under complete and right-censored data. The usefulness of the procedure is also illustrated on real medical data sets, including leukemia, liver cancer, and lung cancer patient survival times, and COVID-19 deaths data. The results indicate the applicability and success of the proposed method in detecting deviations from exponentiality. Overall, this research contributes a handy statistical method for reliability, risk analysis, and medical survival analysis, where system aging is of the utmost importance.