Multivariate Models and the First Four Moments

Several extensions of the multivariate normal model have been shown to be useful in practical data analysis. Therefore, tools to identify which model might be appropriate for the analysis of a real data set are needed. This paper suggests the simultaneous use of two location and two scatter functionals to obtain multivariate descriptive measures for multivariate location, scatter, skewness and kurtosis, and shows how these measures can be used to distinguish among a wide range of models that extend the multivariate normal model. The method is demonstrated with examples on simulated and real data.