Stereology of Extremes; Shape Factor of Spheroids

Abstract

In the stereological unfolding problem of size and shape factor of spheroidal particles the extremal shape factor is investigated. The transformation of particle parameters is shown to be stable with respect to the domain of attraction in three situations: (a) Conditional distribution of shape factor given particle size. (b) Conditional distribution of shape factor given particle section size. (c) Marginal distribution of shape factor. In situation (a) the normalizing constants are derived in a parametric model, which enables prediction of extreme shape factor after a preliminary solution of the size unfolding problem. In both situations (b) and (c) obtaining a similar procedure is still an open problem. The uniformity conditions necessary for (b) and (c) are shown to be mild.