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

Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i Tecnología.