The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach
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The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used
to look at the Dirichlet family of distributions from a new perspective. A classical
Dirichlet density function is expressed with respect to the Lebesgue measure on real
space. We propose here to change this measure by the Aitchison measure on the
simplex, and study some properties and characteristic measures of the resulting density
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