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在M.Jahangir以常数为权的组合式矩估计器的基础上,给出一种以函数为权的组合式矩估计器,称为L-J估计器.其中,最优加权函数是根据U估计器与形状参数的单调关系,通过数论网格最优化算法搜索解出.大量仿真实验证实,在对K分布形状参数v大范围的参数估计中,L-J估计器在估计精度上,不但较Jahangir等提出的常数加权组合矩估计器的精度有显著提高,而且可与MLE(Maximum Likelihood Estimator)相当.特别是由于MLE作为渐进无偏估计量,需要充分大的样本长度才能达到最优,这就使得L-J估计器的估计精度可在样本长度较小时优于MLE.此外,L-J估计器无需迭代运算,因而在计算效率上,显著优于现有的ML估计器.
On the basis of M.Jahangir modular moment estimator with constant weight, a kind of combinatorial moment estimator with function as the weight is given, which is called LJ estimator. The optimal weighting function is based on U estimator Monotonous relationship with the shape parameters, search and solve through the number theory mesh optimization algorithm.A large number of simulation experiments confirm that in the large range of parameter estimation of K distribution shape parameter v, LJ estimator is not only more accurate than Jahangir et al The accuracy of the weighted moment estimator is significantly improved and comparable to that of the Maximum Likelihood Estimator (MLE), especially since MLE as a gradual unbiased estimator needs a sufficiently large sample length to achieve optimal results, which makes LJ The estimation accuracy of the estimator can be better than that of the MLE when the sample length is small. In addition, the LJ estimator does not need iterative computation, so it is significantly superior to the existing ML estimator in computational efficiency.