Maxwell分布的图像特征及统计分析

Image Features and Statistical Analysis of Maxwell Distribution

针对Maxwell分布,首先,考察了Maxwell分布的图像特征,从理论上证明了失效率函数、平均失效率函数和平均剩余寿命函数的单调性;其次,在全样本场合下,给出了尺度参数的极大似然估计、矩估计,考察了估计的无偏性,证明了估计的相合性,并通过模拟比较了点估计的优劣;然后,还给出了求尺度参数区间估计的3种方法,通过模拟比较了区间估计的优劣;最后,通过模拟算例及实例分析说明了所提出方法的适用性,具有一定的实用价值。

For the Maxwell distribution,the image features of the Maxwell distribution are firstly investigated,and the monotonicity of the failure rate function,the average failure rate function and average remaining life function are proved theoretically.Secondly,in the case of full sample,the maximum likelihood estimation and moment estimation of the scale parameter are given,the unbiasedness of the estimations is investigated,the consistency of the estimations is proved,and the advantages and disadvantages of the point estimation are compared by simulation.Then,three methods for interval estimates of scale parameters are given,and the advantages and disadvantages of interval estimates are compared through simulations.Finally,the applicability of the proposed method is illustrated by simulation and arithmetic example analysis,which has certain pratical value.