A Bayesian Shrinkage Approach for the Inverse Weibull Distribution under the Type-II Censoring Schemes (Contemporary Mathematics, 2024)
One main challenge in the application of the lifetime distribution models, such as inverse Weibull (IW) distribution is the need for an appropriate estimation method based on experimental conditions. When prior information and certain guessed values are available for model parameters the Bayesian shrinkage (BS) method becomes a valuable approach in this situation. This study considered the BS estimation method in the two-parameter IW distribution under the squared error loss function (SELF) and the type-II censored data. The maximum likelihood (ML), the least squares (LS), and Bayes estimation methods were also examined for a comparative study. Due to the complexity of calculations, the Lindley approach was utilized to approximate the Bayes estimates. The BS estimates were derived and a score test for the guessed value was presented. Additionally, a Monte Carlo simulation was conducted to evaluate the efficiency of all estimation methods. Furthermore, a real data set was implemented to illustrate and compare the BS estimates with the other estimates. The simulation study indicated the consistency of the estimators. The numerical studies also demonstrated that the BS estimators outperform the others.
Keywords: inverse Weibull, bayes estimation, bayesian shrinkage estimation, lindley approximation, type-II censored data, least squares estimation, maximum likelihood estimation