Prediction and estimation problems in extrem value theory.
Project/Area Number  09680310 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Statistical science

Research Institution  Kobe University of Mercantile Marine 
Principal Investigator 
TAKAHASHI Rinya Kobe University of Mercantile Marine, Fuculty of Mercantile Marine, Professor, 商船学部, 教授 (80030047)

CoInvestigator(Kenkyūbuntansha) 
SIBUYA Masaaki Takachiho University, Professor, 教授 (20146723)

Project Period (FY) 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  extreme value theory / generalized gamma distribution / prediction / return level / stereology / Wicksell's corpuscle problem 
Research Abstract 
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. 1. The size of the spheres is assumed to follow the genelalized gamma distribution with known shape parameters. 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 gamma largest sizes and the total number of the sectional circlesis recommended, because of its satisfactory performance. 2. The size of the spheres is assumed to follow the threeparameter generalized gamma distribution. Prediction methods based on the moment estmation are proposed and there performances are evaluated by simulation. For a practically probable case, one of the these prediction methods is as good as a method previously proposed by us where the two shape parameters are assumed to be known. 3. The size of the spheres which exceed a threshold is assumed to follow the exponential distribution. The return level of random spheres in a volume part is to be predicted from the sectional circular data which exceed the threshold. Prediction method is proposed and its performance is evaluated by simulation.

Report
(3results)
Research Output
(9results)