1996 Fiscal Year Final Research Report Summary
Extreme value theory in stereology and its application.
| Project/Area Number |
06680285
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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, Fuculty of Mercantile Marine, Professor, 商船学部, 教授 (80030047)
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| Co-Investigator(Kenkyū-buntansha) |
SIBUYA Masaaki Takachiho University, Professor, 教授 (20146723)
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| Project Period (FY) |
1994 – 1996
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| Keywords | extreme value theory / generalized gamma distribution / prediction / record-breaking / stereology / unfolding / Wicksell's corpuscle problem |
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| Research Abstract |
Extreme value theory in Wicksell's corpuscle problem, that is, the classical problem in stereology, and its application were mainly studied.
Suppose spherical particles with random sizes are randomly scattered in a space, the spheres being cut by a sectioning plane and we can only observe the sectioning circles : 1. It was proved that the distribution of the size of the sphere and it's Wicksell transformation belong to the same type of extreme value distributions. Some related results were also proved. 2. A problem to predict the maximum size of the spheres in a given volume was investigated. Some possible kinds of measurement of sectioning planes and corresponding prediction methods were proposed. The performance of the prediction methods was studied by simulations. 3. The reason why Wicksell's corpuscle prooblem is ill-posed was shown. Classical methods of unfolding were reviewed and some improvements of those methods were proposed.
For analyzing record statistics, a statistical model and methods for the prediction of future record-breakings were proposed. The methods were applied to some practical data.
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