Bayesian Inference on the Inverse Weibull Model Parameters Based on Kernel Prior

Abstract

Abstract In this paper, the theory of statistical kernel density estimation has been used for deriving the kernel prior, which frees the Bayesian inference from subjectivity to a personal choice that has worried some statisticians. For measuring the performance of the informative kernel prior compared to the informative gamma prior, the mean squared error and mean percentage error have been obtained, via Monte Carlo simulations, for the inverse Weibull model parameters. The simulation results indicated that the informative kernel prior competes with and outperforms the informative gamma prior for different sample sizes. Finally, a numerical example is given to illustrate the proposed priors developed in this paper.