The Study About The Properties And The Bayes Estimation Of The Parameter For Burr Distribution

The Burr distribution has been widely used in social sciences, economic sciences, insurance, actuarial theory and other fields since1942, and it has aroused extensive attention. The parameter estimation is an important part of statistical inference. It is valuable to study the parameter estimation of the Burr distribution.In this paper, we study the Bayes estimation and minimax estimation of the Burr distribution under two loss functions. Firstly, we show the Q-symmetric entropy loss function, and study the Bayes estimation of the parameter for Burr distribution of the conjugate prior distribution under this loss function. We study the minimax estimation by the property of the Bayes estimation. Secondly, we show the scale squared loss function, and study the Bayes estimation of the parameter for the Burr distribution under the scale squared loss function, and give the minimax estimation under the loss function L2.