条件泊松抽样下的经验Bayes概率分布置信域估计

Confidence Region Estimation of Empirical Bayes Probability Distribution Under Conditional Poisson Sampling

采用Mlinex损失函数优化传统损失函数,获取条件泊松抽样下的经验Bayes概率分布置信域估计区间,以及先验分布式逆Gamma分布情况下的后验密度函数,依据该后验密度函数获取参数的Bayes估计,证明该Bayes估计的可容许性,并在置信水平1-α情况下,获取参数的Bayes置信下限和最高后验区间估计.实验结果表明,该方法的估计精确度和运算效率较高,有较强的稳定性.

The paper uses traditional loss function,under the Mlinex loss function,the empirical Bayes probability distribution and the confidence region estimation interval are obtained under conditional Poisson sampling,posterior density function is obtained in a case of prior distributed inverse Gamma distribution.Bayes estimator of the parameter is obtained based on the posterior density function,and the admissibility of the Bayes estimator is proved.In the case of confidence level 1-α,the lower confidence limit of Bayes and the highest posterior range estimation are obtained.The experimental results show that the proposed method has higher estimation accuracy and computational efficiency,and has stronger stability.