Prediction of the Maximum Size in Wicksell's Corpuscle Problem, II

Authors: Takahashi R.¹; Sibuya M.²

Source: Annals of the Institute of Statistical Mathematics, Volume 53, Number 3, 2001 , pp. 647-660(14)

Publisher: Springer

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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.

Keywords: Extreme value theory; generalized gamma distribution; Gumbel distribution; metal fatigue; stereology

Language: English

Document Type: Regular paper

Affiliations: 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

Publication date: 2001-01-01