Classical and Bayesian Methodology for a New Inverse Statistical Model

ABSTRACT This article introduces a two‐parameter statistical model derived by applying an inverse transformation to the cumulative distribution function of the Pham distribution. The proposed model offers a flexible and tractable framework for modeling skewed and heavy‐tailed data, making it well‐suited for applications in reliability engineering, survival analysis, and related fields. We derive key statistical properties of the model, including the quantile function, moments, and the moment‐generating function. Furthermore, we assess the performance of fifteen different estimation methods through extensive simulations to identify the most efficient techniques for parameter estimation. The practical utility of the proposed model is demonstrated using real‐life datasets, where it outperforms several existing competing models. Also, Bayesian inference is implemented in the application section to provide a more comprehensive analysis. The results underscore the model's flexibility, robustness, and computational efficiency in real‐world settings.