一种加权对称损失函数下一类指数分布模型参数的估计

对刻度参数指数分布模型c(x,n)θ-v e-T(x)/θ提出了一种新的损失函数——加权p,q对称熵损失函数L(θ,δ)=θp/pδp +δq/qθq -2(p,q＞O,q＜v),并用它研究了刻度参数θ的估计.得到了参数θ的最小风险同变估计与Bayes估计的一般形式与精确形式,这两种估计形式比已有文献中相应形式更为简捷...

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,q>0,q<ν) 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.