The starting point is that the observed data have a multivariate distribution, and that if there are multiple groups or clusters in a sample, then each group has its own distribution with group-specific means and covariance matrices. The joint distribution is called a mixture distribution. It is important to note that mixture distributions are used not only to model clusters in a population but also to approximate distributions that do not have a known functional form (e.g. skewed distributions) (Titterington et al. 1985). This is illustrated in Fig. 4, which shows that the same observed skewed distribution can be due to either a mixture of three components with equal variance or two components with unequal variance. The mixture components do not necessarily have to correspond to meaningful clusters of subjects in a population. It is for the researcher to decide whether the clusters are meaningful; for instance, whether subjects in the tail of the skewed distribution in Fig. 4 should be considered as a meaningful distinct group. When selecting a model with multiple clusters as the best-fitting model, it is
