GENERAL EXPONENTIAL MODELS ON THE UNIT SIMPLEX AND RELATED MULTIVARIATE INVERSE GAUSSIAN DISTRIBUTIONS

Barndorff-Nielsen and Jorgensen (1989) have introduced some parametric models on the unit simplex. The distributions associated with these models have been obtained by conditioning on the sum of d independent generalized inverse Gaussian random variables. We use a constructive approach to derive some of these models by first mapping the inverse Gaussian law on (0, 1) and formally extending it on the unit simplex. This technique is then applied to a mixture-inverse Gaussian distribution studied recently by Jorgensen, Seshadri and Whitmore (1991). The distributions are then retransformed to yield two versions of a multidimensional inverse Gaussian distribution.