A Comparison of the Bayesian and Other Methods for Estimation of Reliability Function for Burr-XII Distribution

Problem statement: The Burr-XII distribution has been widely used especially in the modeling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood and median estimates with the Bayesian estimate of Reliability function for the two parameter Burr-XII distribution. Approach: The maximum likelihood estimation, median estimation, Bayesian using Jeffrey prior, modified Jeffery prior and extension of Jeffery prior information for estimation the Reliability function of Burr-XII distribution of life time are presented. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the Integrated Mean Square Error (IMSE) and Integrated Mean Absolute Percentage Error (IMAPE). Results: For all the varying sample size, several values of the shifting parameter for the two parameter Burr-XII distribution and for the values for the extension of Jeffery prior, the estimator of Bayesian methods result in smaller IMSE compared to the classical methods in majority of the cases especially in small size of shape parameter. Also in all cases for both methods the IMSE and IMAPE decreases as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of reliability function for the two parameter Burr-XII distribution is found to be superior compared to the conventional methods with respect to IMSE values.