Schl\'omilch integrals and probability distributions on the simplex

Autor:	Chow, David D. K.
Rok vydání:	2022
Předmět:	Mathematics - Probability Mathematics - Classical Analysis and ODEs Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 30 pages; v2, v3: references added, minor changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.11013 Zobrazit plný text záznamu View this record from Arxiv