On the estimation of parameters of a spheroid distribution from planar sections

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-direction distribution of the observable ellipses in the plane into the joint size-shape-direction 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.