2003 Fiscal Year Final Research Report Summary
Prediction in Wicksell's Corpuscle Problem.
| Project/Area Number |
13680373
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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 |
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Principal Investigator |
TAKAHASHI Rinya Kobe University, Faculty of Maritime Sciences, Professor, 海事科学部, 教授 (80030047)
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| Co-Investigator(Kenkyū-buntansha) |
SIBUYA Masaaki Takachiho University, Faculty of Business Management, Professor, 経営学部, 教授 (20146723)
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| Project Period (FY) |
2001 – 2003
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| Keywords | extreme value theory / Gumbel distribution / prediction / quantile / return level / r largest observations / stereology |
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| Research Abstract |
1.The fatigue strength of high-strength steel is closely related to the largest size of non-metallic inclusions in the region of maximum stress of the steel. Hence, it is necessary to predict the largest size of the inclusions based on the size data measured in microscopic view-fields of planar sections of a specimen. A statistical problem is the inference on the distribution of unmeasurable extreme values from the observations on its Wicksell transform. The authors' previous works based on a parametric model are reviewed, and current research activities based on alternative models are introduced.
2.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 sections of spheres cut by a plane. If the area of the great circle of spheres have the exponential tail, simple prediction methods are applied. Performance of the methods is evaluated by simulation and they are applied to a dataset of graphite nodule sizes in spheroidal graphite cast iron.
3.Suppose that larger values are observed in n unit areas or intervals. To estimate quantiles of small upper tail probability, r largest values of n datasets are used. The asymptotic efficiency of the maximum likelihood estimates relative to that of r=1, are shown in Tables. The depth of small pits by corrosion are analyzed along the discussions.
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