Linex损失函数下Laplace分布尺度参数的Bayes估计

Bayes Estimation of the Scale Parameter in the Laplace Distribution Under the Linex Loss Function

在经典贝叶斯统计推断与统计的决策中,Bayes估计的性能主要取决于损失函数的形式,先验分布的不同也会对Bayes估计的结果产生差别。在Linex损失函数下,基于Bayes方法研讨Laplace分布的尺度参数估计。当Laplace分布中位置参数已知时,分别取无先验信息和先验分布为倒伽马分布,计算尺度参数的Bayes估计精确形式和性质,证明了Bayes估计具备可容许性。

In classical Bayesian statistical inference and statistical decision-making,the performance of Bayesian estimation mainly depends on the form of loss function,and different prior distributions will also produce different results.The scale parameter estimation of Laplace distribution is studied based on Bayes method under Linex loss function.When the position parameters in Laplace distribution are known,the exact form and properties of Bayes estimation for scale parameters are obtained by taking no prior information and prior distribution as inverted gamma distribution respectively,thus proving that the estimation is admissible.