Nonparametric hypothesis testing for UB A mgf class of lifetime distribution based on the moment inequality with real-world applications

To test the exponentiality hypothesis against the ‘Used Better Than Aged’ in the moment generating function (UBAmgf) class of life distributions, this work presents a novel statistical test based on moment inequalities. The test was developed in response to the requirement for a strong approach to examining failure behaviour in survival data, particularly in contexts where standard parametric assumptions may not be valid. Extensive statistical investigations were carried out to illustrate the proposed test's performance, including a comparison of its power with that of existing tests over various well-known distribution classes. Critical values were calculated for various significance levels in order to verify its reliability. The test's usability was further validated by applications to both complete and censored survival datasets, ensuring its adaptability to a wide range of real-world situations. Finally, the test was used on a variety of real datasets, demonstrating its usefulness in medical research, particularly in determining the efficacy of therapeutic treatments.