两参数Lomax分布形状参数的经验Bayes估计问题

Empirical Bayes estimation problem of shape parameter of Lomax distribution

依据经验Bayes(EB)估计的思想方法,研究在平方损失函数下两参数Lomax分布形状参数的EB估计问题。在这种损失函数下,获得了形状参数的Bayes估计,利用密度函数的递归核估计方法构造了相应的EB估计,在适当的条件下证明了所提出的EB估计是渐近最优的,并获得了它的收敛速度。最后给出一个满足文中主要结果的实例。

Based on the method of thinking of empirical Bayes（EB） estimator,the EB estimation problem of the shape parameter of Lomax distribution is investigated.Bayes estimator of the shape parameter is obtained with quadratic｜ loss function,and the corresponding EB estimator is constructed by the recursive kernel estimate of probability density function.It is shown that the asymptotically optimal property and convergence rate of proposed EB estimator are obtained under suitable conditions.Finally,an example about the main results of this paper is given.