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Prediction of the maximum size in Wicksell’s corpuscle problem. (English) Zbl 0986.62075
Summary: In the Wicksell corpuscle problem [S. D. Wicksell, Biometrika 17, 84–99 (1925; JFM 51.0392.02)] 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.

MSC:
62M30 Inference from spatial processes
60D05 Geometric probability and stochastic geometry
62M99 Inference from stochastic processes
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