A comparison of some methods for estimating mixed normal distributions

Fisher's method of maximum likelihood breaks down when applied to the problem of estimating the five parameters of a mixture of two normal densities from a continuous random sample of size n. Two alternative methods, (i) moment estimates and (ii) multinomial maximum likelihood and niinimum x2 estimates obtained by grouping the underlying variable, are compared both for bias to n⊟θ1 and mean squared error to n⊟θ2 for a variety of mixed distributions. The methods do not differ essentially with regard to bias but for the mean squared error, the grouped estimates are shown to be more accurate than the moment estimates for most distributions, though the moment estimates seem preferable for distributions which are particularly difficult to estimate. It is also found that the accuracy levels of the grouped maximum likelihood and minimum X2 estimates do not differ greatly.