Some theoretical results on the tensor elliptical distribution

The multilinear normal distribution is a widely used tool in the tensor analysis of magnetic resonance imaging (MRI). Diffusion tensor MRI provides a statistical estimate of a symmetric 2nd-order diffusion tensor for each voxel within an imaging volume. In this article, tensor elliptical (TE) distribution is introduced as an extension to the multilinear normal (MLN) distribution. Some properties, including the characteristic function and distribution of affine transformations are given. An integral representation connecting densities of TE and MLN distributions is exhibited that is used in deriving the expectation of any measurable function of a TE variate.