(untitled) (Statistics, Optimization & Information Computing, 2025)
This study focuses on a new category of life distribution known as the ’Exponential Better than used in convex in Moment Generating Function’ class denoted by . An analysis is conducted based on Laplace transform order for hypothesis testing. The study involves calculating Pitman’s asymptotic efficiencies for this method and comparing them with other approaches. Moreover, a detailed table of percentiles is presented for the statistical measure linked to this proposed technique. Power calculations are performed to assess the effectiveness of the testing methodologies. Additionally, an evaluation is carried out for a test that discriminates exponentiality within right censored data. The power calculations for these tests are derived using simulations with commonly utilized distributions in reliability studies. Finally, actual datasets are employed to illustrate the implementation of the suggested test statistic in addressing practical challenges associated with complete and incomplete data in the field of reliability analysis.