On mixtures of three normal populations caused by monogenic inheritance: application to desipramine metabolism

For a mixture of three normal distributions, which represent genotypes AA, Aa and aa, a method of estimation of the seven unknown parameters is proposed which works well whenever the phenotype (aa) is sufficiently well separated from the phenotype (AA, Aa). It is based on p-values of Kolmogorov's test of goodness of fit to normality. Initial parameter values for this iterative algorithm can be found by visual check and/or by using the EM algorithm. In an example of a data set of size 59 from a study of the metabolic rate of desipramine, the usefulness of this method is demonstrated. Extensions to more complex situations are feasible and are indicated at the end.