an:05204452
Zbl 1315.60023
Mateu-Figueras, Gl??ria; Pawlowsky-Glahn, Vera
The skew-normal distribution on the simplex
EN
Commun. Stat., Theory Methods 36, No. 9, 1787-1802 (2007).
00212546
2007
j
60E05
Aitchison geometry; constrained sample space; random composition
Summary: Density functions on the simplex defined with respect to the Lebesgue measure can change from unimodality to multimodality with perturbation. This phenomenon is induced by the incompatibility of the Aitchison geometry and the Lebesgue measure. A Lebesgue-type measure, compatible with the algebraic geometric structure of the simplex, is used here to define the skew-normal density on the simplex as the Radon-Nykodym derivative with respect to it. Similarities and differences between the densities obtained using the different measures are analyzed.