A Unified Family for Generating Probabilistic Models: Properties, Bayesian and Non-Bayesian Inference with Real-Data Applications

This paper introduces a new generator called the inverse-power Burr–Hatke-G (IPBH-G) family. The special models of the IPBH-G family accommodate different monotone and nonmonotone failure rates, so it turns out to be quite flexible family for analyzing non-negative real-life data. We provide three special sub-models of the family and derive its key mathematical properties. The parameters of the special IPBH-exponential model are explored from using eleven frequentist and Bayesian estimation approaches. The Bayes estimators for the unknown parameters are obtained under three different loss functions. Numerical simulations are performed to compare and rank the proposed methods based on partial and overall ranks. Furthermore, the superiority of the IPBH-exponential model over other distributions are illustrated empirically by means of three real-life data sets from applied sciences including industry, medicine and agriculture.