Decomposition of symmetric multivariate density function

Abstract

For a T-variate density function, the present article denes the quasi-symmetry of order k (< T) and the marginal symmetry of order k, and gives the theorem that the density function is T-variate permutation symmetric if and only if it is quasi-symmetric and marginal symmetric of order k. The theorem is illustrated for the multivariate normal density function. AMS 2010 Mathematics Subject Classication. 62H17.