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arXiv · 2201.11013

Schl\"omilch integrals and probability distributions on the simplex

David D. K. Chow
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Abstract

The Schl\"omilch integral, a generalization of the Dirichlet integral on the simplex, and related probability distributions are reviewed. A distribution that unifies several generalizations of the Dirichlet distribution is presented, with special cases including the scaled Dirichlet distribution and certain Dirichlet mixture distributions. Moments and log-ratio covariances are found, where tractable. The normalization of the distribution motivates a definition, in terms of a simplex integral representation, of complete homogeneous symmetric polynomials of fractional degree.

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David D. K. Chow. 2022-01-26. Schl\"omilch integrals and probability distributions on the simplex. https://arxiv.org/abs/2201.11013

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