Bayesian and classical inference for a novel model: medical and economical real data analysis

In the literature on distribution theory, numerous probability distributions are applied to predict and model real-world phenomena across diverse applied domains, including the medical and healthcare sectors. In the present paper, we develop a new distributional method, referred to as the new exponential power function distribution. The introduced model is incorporated using the transformed-transformer (T-X) approach. The density function of the newly presented distribution is investigated graphically, revealing three distinct patterns, namely symmetric, asymmetric, complex, and skewed shapes. Similarly, the hazard function patterns of the proposed model are also illustrated, which capture the increasing, unimodal, decreasing, and increasing shapes. Further, we developed several key properties such as the moments, quantile function, moment-generating function, and order statistics. Several classical and Bayesian estimation parameters of the new distribution are provided. A Monte Carlo simulation study is conducted to assess the efficiency of these estimators. Lastly, the practicality and efficiency of the novel distribution were validated using four datasets. It is found that the proposed distribution efficiently analyzed these datasets compared with competitive distributions.