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We present an elementary non-recursive formula for the multivariate momentsof the Dirichlet distribution on the standard simplex, in terms of the patterninventory of the moments' exponents. We obtain analog formulas for themultivariate moments of the Dirichlet-Ferguson and Gamma measures. We furtherintroduce a polychromatic analogue of Ewens sampling formula on colored integerpartitions, discuss its relation with suitable extensions of Hoppe's urn modeland of the Chinese restaurant process, and prove that it satisfies an adaptednotion of consistency in the sense of Kingman.

Multivariate Dirichlet Moments and a Polychromatic Ewens Sampling Formula