Advancements in Laplace transform techniques: Performing non-parametric hypothesis testing on real-world data through statistical analysis

Abstract

This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test’s statistical power and explores Pitman’s asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios.