Point-Symmetric Multivariate Density Function and Its Decomposition

Abstract EN

For a T -variate density function, the present paper defines the point-symmetry, quasi-point-symmetry of order k ( < T ), and the marginal point-symmetry of order k and gives the theorem that the density function is T -variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of order k .

The theorem is illustrated for the multivariate normal density function.