COMPUTATIONAL ASPECTS OF FITTING A MIXTURE OF 2 NORMAL-DISTRIBUTIONS USING MAXIMUM-LIKELIHOOD

Fitting a mixture of both two normal distributions and a single normal distribution to empiric data is necessary to construct the likelihood ratio statistic for testing the hypothesis of a mixture of two normals versus a single normal distribution. This problem is particularly troublesome because the iterative maximization methods necessary to compute the maximum likelihood often converge to a.local rather than the global maximum. Simulation was used to explore two issues; 1) which maximization method (direct search or variable metric) is better at quickly finding the global maximum, and 2) how many sets of initial estimates are necessary to consistently find the global maximum. It was found that direct search is slow but accurate, whereas variable metric is fast but inaccurate. It was also found that at least three sets of initial estimates are needed to find the global maximum for more than 99% of all samples. A hybrid method consisting of a few initial iterations of direct search followed by variable metric to convergence is almost as accurate as direct search and almost as fast as variable metric.