The Bayesian and Bayesian shrinkage estimators under square error and Al-Bayyati loss functions with right censoring scheme

Abstract

In this paper, the Bayesian and Bayesian shrinkage estimators of the scale parameter of two-parameter exponential distribution are provided based on the square error and Al-Bayyati loss functions and right censoring. Both informative (inverse-Gamma) and non-informative (quasi-density) priors are considered for the scale parameter of two-parameter exponential distribution. The estimators from different loss functions are evaluated against each other via the risk and risk efficiency measures. Based on the simulation scheme and real data set, we compare the proposed estimators under both loss functions with risk and risk efficiency measures, which lead to efficiency of the Bayesian shrinkage estimates under informative prior. In real data analysis, Bayesian and Bayesian shrinkage estimation of the scale parameter for the flood stages data set is considered with both square error and Al-Bayyati loss functions under the right censoring scheme.