Bayesian Analysis Of Shape Parameter Of Pareto Distribution Based On A Symmetric Loss

In practical application,the two-parameter Pareto distribution is widely accepted.In this paper,we will study the form and properties of the estimation of shape parameter in two-parameter Pareto distribution based on weighted symmetric loss function when scale parameters are known.In the framework of Bayesian statistics,we will start from the relationship between various estimators based on the weighted loss function with known scale parameters.By using the properties and methods of Bayesian parameter estimation,the minimum risk invariant estimation of shape parameters of Pareto distribution with two parameters is discussed,its concrete expression is obtained,and its properties are studied.Then the general form of minimum risk equivariant estimation is obtained.By using the generalized estimation of the parameter,the accurate form of the minimum risk equivariant estimation of shape parameters in Pareto distribution can be obtained.Finally,it is proved that the minimum risk equivariant estimation of shape parameter in Pareto distribution can be obtained accurately.Its minimum risk equivariant estimation has the minimum property,and it is also the minimum estimation of shape parameter.We establish the relationships among the minimum risk equivariant estimation,the minimax estimation and the generalized estimation of shape parameters of Pareto distribution.