AISM 53, 647-660

© 2001 ISM

## Prediction of the maximum size in Wicksell's corpuscle problem, II

### Rinya Takahashi^{1} and Masaaki Sibuya^{2}

^{1}Kobe University of Mercantile Marine, 5-1-1,
Fukae-Minami, Higashi-Nada-ku, Kobe 658-0022, Japan

^{2}Takachiho University, 2-19-1 Ohmiya, Suginami-ku, Tokyo
168-8508, Japan

(Received May 28, 1998; revised March 9, 2000)

Abstract.
This is a continuing paper of the authors (1998, *Ann. Inst. Statist. Math.*, **50**, 361-377). In the Wicksell
corpuscle problem, the maximum size of random spheres in a volume
part is to be predicted from the sectional circular distribution of
spheres cut by a plane.
The size of the spheres is assumed to follow the three-parameter
generalized gamma distribution.
Prediction methods based on the moment estimation are proposed and
their performances are evaluated by simulation. For a practically
probable case, one of these prediction methods is as good as a method
previously proposed by the authors where the two shape parameters
are assumed to be known.

Key words and phrases:
Extreme value theory, generalized
gamma distribution, Gumbel distribution, metal fatigue, stereology.

**Source**
(TeX , DVI )