Stereology of extremes; shape factor of spheroids. (English) Zbl 1051.60011

Hlubinka, Daniel

Extremes 6, No. 1, 5-24 (2003).

Ellipsoidal particles of oblate shape are considered, i.e. their two major semiaxes are equal (\(X\)) and one is minor (\(W<X\)). The shape factor is defined as \(T=X^2/W^2-1\). A shape factor of a planar section of such particle is \(Z=Y^2/V^2-1\), where \(Y\) is the major and \(V\) the minor semiaxis of the section. The orientation of the section is assumed isotropic. It is shown that (roughly speaking) if the distribution of \(T\) belongs to a domain of the max-attraction of some max-stable law, then \(Z\) also belongs to the same domain. Gamma distribution of \(T\) is considered as an example.

Reviewer: R. E. Maiboroda (Kyïv)

MSC:

60D05	Geometric probability and stochastic geometry
62G32	Statistics of extreme values; tail inference

Keywords:

oblate shape particle; domain of max attraction; Gamma distribution