Some Methods for Studying the Mixture of Two Normal (Lognormal) Distributions

Abstract This article explores several topics related to the mixture of two normal or lognormal distributions. A study is made of diagnostic plotting procedures for the detection of mixtures, and a new method, the Φ — p versus Q plot, is developed that is more sensitive to the presence of mixtures than more familiar methods. A series of ad hoc methods that produce initial guesses for parameter values is also presented. Two methods of global estimation given initial parameter guesses are presented and compared. These methods are the maximum likelihood and a least squares procedure that fits the sample quantiles to the inverse distribution function of the mixture. The sensitivity of the methods to poor choices for initial guesses is also considered.