具有部分缺失数据的混合幂分布参数估计与检验

Parameter Estimation and Test of Mixed Power Law Distribution with Partially Missing Data

研究了部分数据缺失情况下混合幂分布总体参数的估计及假设检验问题。通过混合幂分布的密度函数和矩估计方程,求解出混合幂分布中参数的矩估计,证明了估计量的强相合性和渐近正态性。同时讨论了单个混合幂分布的存在性检验问题及两个混合幂分布参数相等的检验问题,构造混合幂分布情况下的检验统计量,并给出检验统计量的极限分布。最后,通过随机模拟验证了估计量的有效性,根据不同样本量及数据缺失比例不同情况下的模拟结果对矩估计方法的可行性进行说明。

This paper studies the estimation and hypothesis test of population parameters of Mixed Power Law Distribution under the condition of partial data missing.By solving the moment estimation of the parameters in the Mixed Power Law Distribution by the density function and the moment estimation equation of the Mixed Power Law Distribution,the strong correspondence and asymptotic normality of the estimator are proved.At the same time,the existence test of single Mixed Power Law Distribution and the test of equal parameters of two Mixed Power Law Distributions are discussed.The test statistics in the case of Mixed Power Law Distribution are constructed,and the limit distribution of the test statistics is given.Finally,the validity of the estimator is verified by random simulation,and the feasibility of the moment estimation method is explained according to the simulation results under different sample sizes and data deletion ratios.