A Monte Carlo Investigation Of The Likelihood Ratio Test For The Number Of Components In A Mixture Of Normal Distributions

A likelihood ratio test to determine whether data arises from a single or a mixture of two normal distributions is investigated by Monte Carlo methods. The results show that the proposed sampling distribution of the test appears to be appropriate only for sample sizes above fifty, and for data where the sample size is ten times the number of variables. For such cases the power of the test is considered and found to be fairly low unless the generalized distance between the components is greater than 2.0.