Comparison between the standard Bayesian method and the hierarchical Bayesian method for estimating the reliability function of the inverse Lomax distribution with type II observational dat

Abstract

In this paper, the shape and size parameters (without imposing either parameter) and the survival function of the inverse Lomax distribution in the presence of observational data of the second type are estimated using different Bayesian methods, which included the standard Bayesian method and the hierarchical Bayesian method under a symmetric loss function, which is the quadratic loss function, and in order to compare The two methods used Monte Carlo simulation, where different sample sizes and three models of default values for distribution parameters (Ѳ,λ) , were used and the statistical measure, mean integral square error (IMSE), was used. Simulation experiments showed the superiority of the hierarchical Bayesian method because it has the least mean square integral error (IMSE)