  We study modeling and inference with the Elliptical Gamma Distribution (EGD).
We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task
for which we develop new fixed-point algorithms. Our algorithms are efficient
and converge to global optima despite nonconvexity. Moreover, they turn out to
be much faster than both a well-known iterative algorithm of Kent & Tyler
(1991) and sophisticated manifold optimization algorithms. Subsequently, we
invoke our ML algorithms as subroutines for estimating parameters of a mixture
of EGDs. We illustrate our methods by applying them to model natural image
statistics---the proposed EGD mixture model yields the most parsimonious model
among several competing approaches.
