Estimation in Mixtures of Two Normal Distributions
Estimation in Mixtures of Two Normal Distributions
复制标题
两种正态分布混合的估计
DOI：
10.1080/00401706.1967.10490438
复制
发表时间：
1967
期刊：
影响因子：
2.5
通讯作者：
A. Clifford Cohen
中科院分区：
文献类型：
--
作者：
A. Clifford Cohen
本文主要讨论矩的方法在解剖两个正态分布的混合物。在一般情况下，有两个均值，两个标准差和一个比例因子要估计，前五个样本矩是必需的，并且有必要找到一个九次多项式方程的特解，这个方程最初是由卡尔·皮尔逊（Karl Pearson）推导出来的。提出了一种绕过非方程求解的方法，从而大大减少了所需的总计算量。在假设两个标准差相等的较简单的特殊情况下得到的估计，作为迭代方法中的第一近似，用于同时求解适用于两个标准差不等的更一般情况的基本力矩方程组。条件最大似然和条件最小卡方估计，前提是前四个样本矩相等。
This paper is concerned primarily with the method of moments in dissecting a mixture of two normal distributions. In the general case, with two means, two standard deviations, and a proportionality factor to be estimated, the first five sample moments are required, and it becomes necessary to find a particular solution of a ninth degree polynomial equation that was originally derived by Karl Pearson [10]. A procedure which circumvents solution of the nonic equation and thereby considerably reduces the total computational effort otherwise required, is presented. Estimates obtained in the simpler special case in which the two standard deviations are assumed to be equal, are employed as first approximations in an iterative method for simultaneously solving the basic system of moment equations applicable in the more general case in which the two standard deviations are unequal. Conditional maximum likelihood and conditional minimum chi-square estimation subject to having the first four sample moments equated ...