  We study two different methods for inferring the parameters of a spheroid
distribution from planar sections of a stationary spatial system of spheroids:
one method first unfolds non-parametrically the joint size-shape-orientation
distribution of the observable ellipses in the plane into the joint
size-shape-orientation distribution of the spheroids followed by a maximum
likelihood estimation of the parameters; the second method directly estimates
these parameters based on statistics of the observable ellipses using a
quasi-likelihood approach. As an application we consider a metal-matrix
composite with ceramic particles as reinforcing inclusions, model the
inclusions as prolate spheroids and estimate the parameters of their
distribution from planar sections.
