Maximum Likelihood Estimation for Mixtures of Two Normal Distributions
Nathan P. Dick, David C. Bowden · Biometrics · 1973
This paper is primarily concerned with estimation of the parameters 1, al2 /-2 a22 and p in the mixture of two normal distributions when independent sample information is available from one of the populations. The solution to the maximum likelihood (ML) equations was obtained using Newton's iterative method. Some interesting results for the moment estimates were obtained for the case when independent sample observations are available from one population. Extensive Monte Carlo simulation was employed to obtain the sample variances of the estimates as well as the estimated asymptotic variances. The variances of the estimates are influenced by the separation of the two means with respect to the variances, the mixture proportion (p), and, of course, the size of the sample. When the number of observations is small and the means are not well separated, the sample variance of the estimates can be as much as three times greater than the estimated asymptotic variances.