Mixtures of multivariate leptokurtic normal distributions

We introduce mixtures of multivariate leptokurtic normal (LN) dis- tributions as a tool for robust model-based clustering in the presence of mild outliers. Comparedtothenormaldistribution, theLNhasanadditionalparameterand, advanta- geously with respect to the existing elliptical heavy-tailed distributions, the additional parameter directly corresponds to the quantity of interest, namely, the excess kurtosis. We outline an EM algorithm for maximum likelihood estimation of the parameters of the mixture. As an illustration, we analyze the well-known Old Faithful geyser data.