| Project/Area Number |
11680322
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Kobe University of Mercantile Marine |
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Principal Investigator |
TAKAHASHI Rinya Kobe University of Mercantile Marine, Faculty of Mercantile Marine, Professor, 商船学部, 教授 (80030047)
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| Co-Investigator(Kenkyū-buntansha) |
SIBUYA Masaaki Takachiho University, Professor, 商学部, 教授 (20146723)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | extreme value theory / exponential distribution / prediction / return level / stereology / Wicksell's corpuscle problem / ウィクセル小球問題 / Wicksell 小球問題 |
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| Research Abstract |
In the Wicksell corpuscle problem, the maximum size of random spheres in a reference volume is to be predicted from the size distribution of circles which are planar section of spheres cut by a plane.
1. 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 theory and simulation. For a practically probable case, one of these prediction methods is as good as a method previously proposed by us where the two shape parameters are assumed to be known.
2. The size of the spheres which exceed a threshold is assumed to follow the exponential distribution. The return level of random spheres in a reference volume is to be predicted from the sectional circular data which exceed the threshold. Simple prediction methods are proposed and their performances are evaluated by simulation and they are applied to a real dataset.
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