A common problem in statistical modelling is to distinguish between finite mixture distribution and a homogeneous non-mixture distribution. Finite mixture models are widely used in practice and often mixtures of normal densities are indistinguishable from homogenous non-normal densities. This paper illustrates what happens when the EM algorithm for normal mixtures is applied to a distribution that is a homogeneous non-mixture distribution. In particular, a population-based EM algorithm for finite mixtures is introduced and applied directly to density functions instead of sample data. This algorithm is used to find finite mixture approximations to common homogeneous distributions. An example regarding the nature of a placebo response in drug treated depressed subjects is used to illustrate ideas.

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统计建模中的一个常见问题是区分有限混合分布和齐次非混合分布。有限混合模型在实践中广泛使用，并且通常正态密度的混合物与齐次非正态密度无法区分。本文说明了将正态混合的 EM 算法应用于齐次非混合分布时会发生什么情况。特别是，引入了一种基于群体的有限混合 EM 算法，并将其直接应用于密度函数而不是样本数据。该算法用于查找常见齐次分布的有限混合近似。一个关于药物治疗的抑郁症受试者中安慰剂反应的性质的例子被用来说明想法。