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Burr distribution with two parameters was first introduced by Burr. This distribution has gained special attention and has been applied in various disciplines. To find out more about the characteristics of the data having Burr distribution, the parameters of Burr distribution need to be estimated. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. However, the Bayesian approach has received much attention in contention with other estimation methods. The parameter estimation using the Bayesian method not only uses the information from the sample data, but also combines it with the prior information of the parameter. Jeffrey prior is one of the prior information we can use. It is a noninformative prior which is proportional to the square root of the Fisher information. In this paper we consider using Jeffrey prior information to estimate the shape parameter k of Burr distribution. As a comparison, we also use expansion of Jeffrey prior information which is proportional to the positive power of the Fisher information. The comparison was made through a simulation study with respect to the mean-squared error (MSE). The results of comparison show that Bayes estimator for the shape parameter k using Jeffrey prior gives better results if the power in the extension of Jeffrey prior is less than 0.5, while Bayes estimator using the extension of Jeffrey prior gives better results if the power in the extension of Jeffrey prior is more than 0.5. Based on the results of this simulation study, we can conclude that with respect to the mean-squared error, Bayesian estimation for the shape parameter k of Burr distribution using Jeffrey prior information is found to be superior in turn with the extension of Jeffrey prior information depend on the power in the extension of Jeffrey prior.

Bayesian method; Burr distribution; extension of Jeffrey prior information; Jeffrey prior information