Parameter estimation of Burr distribution for right censored data with Bayes method

Abstract

Burr Type XII distribution is known as Burr distribution, is one of the twelve types continuous distribution on Burr system. Burr distribution is heavy-tailed and right-skewed. Burr distribution has an important role in survival analysis. This study will describe parameter estimation of Burr distribution for right censored data using Bayes method. Procedure for estimating parameter consists of three main steps: specifying the prior distribution, constructing likelihood function for right censored data and determining the posterior distribution. Bayes estimator is obtained by minimizing posterior risk function based on loss function, using Square Error Loss Function (SELF) and Precautionary Loss Function (PLF). After Bayes estimator is obtained, simulation will be done to compare the effectiveness of Bayes estimator with both loss function according to Mean Square Error (MSE). What is meant by effective estimator is that it has relatively small MSE. Furthermore, this study also elaborated the effect of the proportion of censored data to the MSE. Based on simulation results, Bayes estimator with PLF is more effective than SELF and higher proportion of censored data produced greater MSE, regardless of the loss function.