Estimation of Parameters for a Mixture of Normal Distributions

n observations are taken from a mixture of K normal subpopulations, where the value of K is known. It is assumed that these n observations are given as N frequencies from equally spaced intervals. Initial guesses of the K means, K variances, and K − 1 proportions are made using the maximum likelihood estimates for a single truncated normal population as derived by Hald. Then an approximation to the likelihood function of the entire sample is used, and attempts to maximize this yield two iteration formulas. In practice, the method of steepest descent always converged, although the rate was not always fast. Special cases of equal variances and variances proportional to the square of the mean are also considered.