Maximum size prediction in Wicksell's corpuscle problem.

威克塞尔小体问题中的最大尺寸预测。

• 批准号: 11680322
• 负责人: TAKAHASHI Rinya
• 金额: $ 1.22万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11680322/
• 关键词: 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

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.

在维克塞尔微粒问题中，参考体积中随机球体的最大尺寸是由球体被平面切割后的平面部分的圆的尺寸分布来预测的。1.球的大小被假定为遵循三参数广义伽玛分布。提出了基于矩估计的预测方法，并通过理论和仿真对其性能进行了评估。对于一个实际可能的情况下，这些预测方法之一是一样好的方法，我们以前提出的两个形状参数假设是已知的。假设超过阈值的球体的尺寸遵循指数分布。参考体积中随机球体的返回水平将从超过阈值的截面圆形数据预测。提出了简单的预测方法，并通过模拟评估其性能，并将其应用于真实的数据集。

项目成果

Takahashi,R.: "Prediction of the maximum size in Wicksell's corpuscle problem II."Annals of Institute of Statistical Mathematics. (掲載予定). (2001)

Takahashi, R.：“Wicksell 粒子问题 II 中最大尺寸的预测”。《统计数学研究所年鉴》（即将出版）。

Takahashi, R.and Sibuya, M.: "Prediction of the maximum size in Wicksell's corpuscle problem II."Annals of Institute of Statistical Mathematics.. (to appear). (2001)

Takahashi, R. 和 Sibuya, M.：“维克塞尔小体问题 II 中最大尺寸的预测。”统计数学研究所年鉴..（待发表）。

Takahashi,R: "Prediction of the maximum size in Wicksell's corpuscle problem II."Annals of Institute of Statistical Mathematics. (掲載予定). (2001)

Takahashi, R：“Wicksell 粒子问题 II 中最大尺寸的预测”。《统计数学研究所年鉴》（即将出版）。