逐步增加Ⅱ型截尾下复合瑞利分布参数的Bayes估计

BAYES ESTIMATION OF COMPOUND RALEIGH DISTRIBUTION PARAMETERS UNDER TYPEⅡTRUNCATION

在逐步增加Ⅱ型截尾样本下,给出了复合瑞利分布尺度参数的极大似然估计.在取先验分布为无先验信息、共轭先验分布、指数分布时,考虑平方损失函数与对称熵损失函数估计的准确性,得到了参数的Bayes估计的表达式.通过随机模拟试验数据对比发现,从有无先验信息的角度看,尺度参数θ的Bayes估计在无先验信息下的估计要更加接近真值,故无先验信息下的估计值比有先验信息的估计值更准确.在不同的损失函数下,对称熵损失函数下的估计值均方误差较小,故在对称熵损失函数下尺度参数θ的估计是最优的.

With the increasing of typeⅡcensored samples,the maximum likelihood estimation of the scale parameters of the composite Rayleigh distribution is given.When the prior distribution is taken as no prior information,conjugate prior distribution and exponential distribution,the accuracy of the estimation of the square loss function and symmetric entropy loss function is considered,and the expression of the Bayes estimation of the parameters is obtained.From the point of view of whether there is prior information or not,the Bayes estimation of scale parameters is closer to the true value without prior information,so the estimation value without prior information is more accurate than that with prior information.Under different loss functions,the mean square error of the estimation value under symmetric entropy loss function is smaller,so the estimation of scale parameters under symmetric entropy loss function is optimal.