q -对称熵损失函数下Pareto分布参数估计

Pareto分布作为一种收入分布有着很重要的现实意义,其形状参数的大小直接影响收入分布的均衡程度,因此在经济中有着广泛的应用价值.主要研究了q-对称熵损失函数下Pareto分布形状参数的最小风险同变估计和Bayes估计.通过证明得到,在适当的Γ-先验分布下,α的Bayes估计都具有统一的形式cT＋d]-1.并且,针对c和d的各种不同取值情况,讨论了cT＋d]-1的可容许性和不可容许性,给出了q-对称熵损失函数下参数的最小最大估计.

Estimation of Pareto distribution parameter under q -symmetric entropy loss function

As an income distribution,the Pareto distribution has a very important practical value.The shape parameter directly affects the balance of the income distribution,so it has extensive applications in economy.Based on the q-symmetric entropy loss function,the minimum risk equivariant（MRE） estimation and the Bayes estimation of the shape parameter of Pareto distribution are studied.The Bayes estimations of α have a unified form cT+d] ₁ with a proper Γ-prior distribution.The admissibility and inadmissibility of these estimations with different values of c and d are discussed.Furthermore,based on the q-symmetric entroy loss function,the minimax estimation of the parameter is given.