Optimizing Analgesic Pain Relief Time Analysis Through Bayesian and Non-Bayesian Approaches to New Right Truncated Fréchet-inverted Weibull Distribution

This research introduces a novel right-truncated distribution, termed the right truncated Fréchet-inverted Weibull distribution, and elucidates its mathematical properties including density, cumulative, survival and hazard functions. Various statistical attributes such as moments, quantile, mode and moment-generating functions are explored. These properties indicate the efficiency in modeling pain relief time for patients and the number of recoveries of Leukemia patients. Furthermore, estimation techniques, including maximum likelihood and Bayesian methods, are applied to progressive type-Ⅱ right-censored samples to derive parameter estimation of the proposed distribution. Asymptotic properties are employed to approximate confidence intervals for both reliability and hazard functions. Bayesian estimates are refined using both symmetric and asymmetric loss functions. The suitability of the proposed estimation methodologies is validated through simulation studies. The theoretical framework is applied to two real-world lifetime data sets, thereby substantiating their practical utility in medical areas.