The Skew-Normal Distribution on the Simplex

What is it about?

The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows us to work with coordinates with respect to an orthonormal basis. Standard real analysis can be applied to the coordinates and probability laws can be defined using distribution functions of the vector of coordinates. Furthermore, densities on the simplex can be considered as Radon-Nikodym derivatives either with respect to the Lebesgue measure or with respect to a measure compatible with the algebraic geometric structure of the simplex. Here, the skew-normal distribution on the simplex is presented, and similarities and differences of the densities obtained with each of the above mentioned measures are analysed.

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