A Novel U-Statistic Test for Exponentiality Against EBUCL Reliability Class and Applied to Complete and Censored Data Across Various Risk Profiles

Statistical testing plays a pivotal role in enabling researchers to draw sound conclusions from data. Nonparametric tests, in particular, are highly valuable due to their flexibility in handling various data sets without requiring assumptions about the underlying distribution. In response to the growing need for robust testing procedures, this study introduces a new classof life distributions known as exponential better than used in convex Laplace transform order (EBUCL). A novel U-statistic-based test is developed to evaluate exponentiality against this class. The asymptotic properties of the proposed test are thoroughly examined, and critical values for sample sizes ranging from 5 to 50 are reported. A detailed simulation study evaluates the test’spower under commonly encountered reliability models. Moreover, Pitman’s asymptotic efficiency is calculated and compared with that of existing methods. The study also extends the methodology to handle right-censored data. Finally, the practical utility of the proposed test is demonstrated through applications to several real-world data sets from diverse fields.