Prediction and estimation problems in extrem value theory.

极值理论中的预测和估计问题。

• 批准号: 09680310
• 负责人: TAKAHASHI Rinya
• 金额: $ 1.15万
• 依托单位: Kobe University of Mercantile Marine
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09680310/
• 关键词: extreme value theory; generalized gamma distribution; prediction; return level; stereology; Wicksell's corpuscle problem

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 three-parameter 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.

在Wicksell小体问题中，体积部分中随机球体的最大尺寸是根据球体被平面切割的截面圆形分布来预测的。假设球体的大小服从具有已知形状参数的广义伽马分布。根据截面上的测量方法提出了几种预测方法，并通过仿真对其性能进行了评估。推荐采用基于伽马最大尺寸和截面圈数的预测方法，其预测效果较好。假设球体的大小服从三参数广义伽马分布。提出了基于矩估计的预测方法，并对其性能进行了仿真评估。对于实际可能的情况，这些预测方法中的一种与我们先前提出的假设两个形状参数已知的方法一样好。假设超过阈值的球体大小服从指数分布。从超过阈值的截面圆形数据中预测体积部分中随机球体的返回水平。提出了预测方法，并通过仿真对其性能进行了评估。

项目成果

Takahashi, R.and Sibuya, M.: "Prediction of the maximum size in Wicksell's cor-puscle problem." Annals of Institute of Statistical Mathematics. 50. 361-377 (1998)

Takahashi, R. 和 Sibuya, M.：“Wicksell Cor-puscle 问题中最大尺寸的预测。”

Sibuya, Masaaki: "Wicksell´s corpuscle problem." Encyclopedia of Statistical Science, Update Volume, Wiley. (印刷中). (1999)

Sibuya，Masaaki：“Wicksell 的小体问题。”统计科学百科全书，更新卷，Wiley（1999 年出版）。

Takahashi, Rinya: "Prediction of the maximum size in Wicksell's corpuscle problem." Annals of Institute of Statistical Mathematics. 50. 361-377 (1998)

Takahashi, Rinya：“威克塞尔红细胞问题中最大尺寸的预测。”

Sibuya,Masaaki: "Wicksell's corpuscle problem." Encyclopedia of Statistical Sciences,Update Volume,Wiley.(印刷中). (1999)

Sibuya，Masaaki：“威克塞尔的小体问题。”统计科学百科全书，更新卷，威利（1999 年出版）。

Sibuya, M.and Nishimura, K.: "Prediction of record-breakings" Statistica Sinica. 7. 893-906 (1997)

Sibuya, M. 和 Nishimura, K.：“破纪录的预测”《Statistica Sinica》。