Estimator of the Scale Parameter in a Subclass of the Exponential Model under a Weighted Symmetric Loss Function

For scale-parameter exponential model c(x,n)θ-νe-T(x)/θ,we propose a new loss function-weighted p,q symmetric entropy loss function L(θ,δ)=θp/δp+δq/θq-2(p,q0,qν) and investigate the estimator of parameter θ using it.The general form and exact form of the minimum risk equivariant estimator and Bayes estimator which are simpler than those in the literature are obtained.The minimaxity of the minimum risk equivariant estimator and the invariance of the Bayes estimator which have not been discussed in the literature under other loss are proved.Therefore,the content of the scale parameter estimation of the scale-parameter exponential model c(x,n)θ-νe-T(x)/θ is enriched and extended.