Title: Some theoretical results on tensor elliptical distribution,
Abstract: The multilinear normal distribution is a widely used tool in 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.