The additive logistic skew-normal distribution on the simplex

Abstract

There is a dearth of suitable models with which to adequately model compositional data sets, especially those which exhibit skewness after additive logratio-transformation. In order to address this deficit we propose the additive logistic skew-normal distribution, an extension to the additive logistic normal model on the simplex derived from the skew-normal distribution in real space. The purpose of this paper is to outline the potential of this distribution in the modelling of compositional data. We present its most important properties and use an example to exhibit the potential of this distribution.