加权刻度平方误差损失下Rayleigh分布参数的Bayes估计与性质

The Rayleigh distribution parameters under the weighted scale squared error loss Bayes estimation with nature

摘要: 在加权刻度平方误差损失函数下,使用Bayes参数估计方法,研究了Rayleigh分布参数的Bayes估计的形式与性质. 首先在任意先验分布下,得到了参数的Bayes估计的一般形式,然后在逆Gamma先验分布下,得到了参数的Bayes估计的精确形式,证明了所得Bayes估计具有可容许性. 最后利用Matlab进行数据模拟,验证了Bayes估计的合理性.

Abstract: The forms and properties of the Bayes estimation of the Rayleigh distribution parameters were studied by the Bayes parameter estimation method under the weighted scale squared error loss function.First,the general form of the Bayes estimation of the parameters under an arbitrary prior distribution was obtained.Second,the exact form of the Bayes estimation of the parameters under the inverse Gamma prior distribution was obtained,and the admissiblity of the obtained Bayes estimation was proved.Finally,a simulations with Matlab was maded to evalue the obtained Bayes estimation.