###
PREDICTION OF THE MAXIMUM SIZE IN

WICKSELL'S CORPUSCLE PROBLEM

###
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} *Department of Mathematics, Keio University, 3-14-1, Hiyoshi,*

Kohoku-ku, Yokohama 223-8522, Japan
(Received November 29, 1995; revised May 6, 1997)

**Abstract.**
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 generalized gamma distribution.
Some prediction methods according to measurement methods
on the sectional plane are proposed, and their
performances are evaluated by simulation. The prediction
method based on the *r* largest sizes and the total
number of the sectional circles is recommended, because
of its satisfactory performance.

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

**Source**
( TeX ,
DVI ,
PS )