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

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.

### MSC:

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