有Edgeworth展式的分布的随机加权逼近的重对数律

摘要

本文研究了未知分布的逼近问题.利用随机加权法,给出了有Edgeworth展式的一类(未知)分布的模拟分布,证明了在一定条件下,模拟分布与未知分布的逼近精度达到O(n-1√lnlnn),称之为随机加权逼近的重对数律.%In this paper, the approximate problem of unknown distribution is investigated.By using random weighting method, the simulated distribution of unknown distribution admittingEdgeworth expansion is presented. It is proved that under certain conditions, the precision of thesimulated distribution's approximation to unknown distribution reach O(n-1 √ln lnn). It is called thelaw of iterated logarithm of random weighting approximation.