A class of new parametric models on the unit simplex in Rm is introduced, the distributions in question being obtained as conditional distributions of m independent generalized inverse Gaussian random variables given their sum. The Dirichlet model occurs as a special case. Two other special cases, corresponding respectively to the inverse Gaussian model and the reciprocal inverse Gaussian model, are studied in some detail. In particular, several exact chi-squared decompositions are found. © 1991.
Barndorff-Nielsen, O. E., & Jørgensen, B. (1991). Some parametric models on the simplex. Journal of Multivariate Analysis, 39(1), 106–116. https://doi.org/10.1016/0047-259X(91)90008-P