最小二乘法在估计概率分布参数中的应用

提出一种估计概率分布参数的最小二乘法，这种方法以概率密度函数和频率间的关系为基础，通过对概率密度函数和频率间的关系进行合理的近似，建立求解未知分布参数的方程组，在求解过程中，将样本容量视为未知量，以简化求解过程。计算机模拟实例表明，这种方法求解出的未知分布参数精度较高，而且对于一些常见的分布函数，这处方法的求解过程十分简单。文中还通过计算机模拟对本文方法和极大似然估计法做了统计分析。

APPLICATION OF THE LEAST SQUARE METHOD IN THE ESTIMATION OF THE PARAMETERS OF THE PROBABILITY DISTRIBUTION

This paper presents a least square method to estimate the values of the parameters of the probability distribution.The method is based on the relation between the frequency and the probability density function and by a reasonable approach to the relation,the paper establishes equations to solve for the unknown parameters.In the process of the solving the equations,the sample size is considered a unknown parameter to simplify the process.Examples in the paper show that the parameters estimated by the presented method are quite accurate,and the process of the solving the equations is very simple to some common probability distribution functions.Additional,the comparison of statistic analyses of the presented method to the maximum likelihood method is done by the computer simulation.