Recovering the parameters of finite mixtures of normal distributions from a noisy record: an empirical comparison of different estimating procedures.

Three procedures were compared for their ability to estimate the known parameters of mixtures of normal distributions: maximum likelihood estimators (MLE), X2 minimization method and the least-square error procedure. For this purpose a Monte-Carlo study was undertaken to evaluate empirically the performance of the estimators. We chose to investigate their behaviour using closely-positioned mixtures of two or 3 univariate Gaussians. The Monte-Carlo simulations clearly demonstrate the superiority of the MLE and X2 minimum methods. Other reasons why the MLE is to be preferred are discussed. The effect of sample size was also examined. All 3 estimators have also been applied to data derived from different physiological experiments, and the use of the estimators is considered in practical terms. The formulae for all 3 procedures are given in the Appendix.