Using Jeffrey prior information to estimate the shape parameter k of Burr distribution

Burr distribution with two parameters was first introduced by Burr. This distribution has gained special attention and has been applied in various disciplines. The maximum likelihood method is the most commonly used to estimate its parameters. However, the Bayesian method receives more attention. The parameter estimation using the Bayesian method not only uses the information from the sample data but also combines it with the prior information for the parameter. Jeffrey prior information is one of the prior information we can use. This prior is a noninformative prior. It is proportional to the square root of the Fisher information for the parameter. In this paper we use Jeffrey prior information to estimate the shape parameter k of Burr distribution. As a comparison, we also use an extension of Jeffrey prior information which is proportional to the Fisher information raised by a positive constant. The comparison is made through a simulation with respect to the mean-squared error (MSE) and the posterior risk. The results of the comparison show that the Bayesian estimation for the shape parameter k under Jeffrey prior information gives better results in turn with the extended Jeffrey prior information.