Exploring the New Exponentiated Inverse Weibull Distribution: Properties, Estimation, and Analysis via Classical and Bayesian Approaches

The “New Exponentiated Inverse Weibull” (NEIW) distribution is a novel probability distribution with versatile applications in reliability engineering, survival analysis, and related fields. This study explores the properties of the NEIW distribution, including moments, hazard function behavior, and reliability measures, through rigorous theoretical analysis and simulation studies. Additionally, maximum likelihood estimators (MLEs) for NEIW parameters are investigated via simulation studies to evaluate their performance under various scenarios. Empirical analysis using real-world data sets demonstrates the applicability of the NEIW model in capturing the underlying data structure and extracting meaningful insights. Parameter estimation and analysis are conducted using classical and Bayesian approaches, showcasing the robustness and flexibility of the NEIW distribution. The latest Bayesian analysis software STAN is used to perform the Bayesian analysis using Hamiltonian Monte Carlo (HMC) under No-U-Turn Sampler (NUTS). Overall, this research contributes to the advancement of statistical modeling and analysis by providing a comprehensive framework for utilizing the NEIW distribution in practice, with implications for diverse fields and potential for further exploration and innovation.