EM算法在混合正态分布模型参数估计中的应用研究

摘要

有限混合分布可以作为众多随机现象的统计模型。很多随机现象在样本量足够大时都可以用正态分布近似，并且混合正态分布模型具有灵活、高效的拟合能力，因此混合正态分布模型被广泛应用。本文利用EM算法对混合正态分布模型进行了参数估计。该算法利用数据扩张，将比较复杂的似然函数最优化问题化成一系列比较简单的函数优化问题，得到相应的迭代公式。最后通过R软件对EM算法进行数值模拟，验证了EM算法的收敛性和有效性。%Finite mixtures of distributions have provided an approach to the statistical modeling of a wide va-riety of random phenomena. Many random phenomena can be described by normal distribution when their sample sizes are large enough. Mixture normal distribution is widely used in this situation for its flexible and efficient fit-ting ability. In this paper, the parameters of mixture normal distribution are estimated by EM algorithm. The opti-mizations of complex likelihood functions are turned into a series of optimizations of functions by data expansion in this algorithm, which can obtain the corresponding iterative formula. Finally, the simulation results illustrated the algorithm's convergence and effectiveness.