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

TL;DR

This paper compares two statistical methods for estimating the parameters of spheroid distributions from planar sections, applying them to ceramic particle inclusions in a metal-matrix composite.

Contribution

It introduces and compares non-parametric unfolding with a maximum likelihood approach and a direct quasi-likelihood method for spheroid parameter estimation.

Findings

Both methods effectively estimate spheroid parameters from planar sections.

Application to ceramic particles demonstrates practical utility.

The quasi-likelihood method offers a computationally efficient alternative.

Abstract

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.