Improvement of Jahangir’s multiple moments estimator

Based on M.Jahangir-s multiple moments estimator using constant weight, a new estimator named L-J estimator was proposed, which consists of multiple moments and uses function weight. The optimum weight function was obtained by the sequential algorithm for optimization according to the monotonic relationship of U-estimator and the shape parameter. A large number of simulation experiments show that the accuracy of L-J estimator is not only higher than that of Jahangir-s multiple estimator using constant weight noticeably, but also it can stand comparison with that of maximum likelihood estimator (MLE). As an asymptotic unbiased estimation, MLE requires sufficient large number of samples to achieve the optimum performance, then it makes that the accuracy of L-J estimator can be better than that of MLE in the case of fewer samples. Moreover, the efficiency of L-J estimator is obviously higher than that of MLE, since there is no iteration to need.