Extreme value theory in stereology and its application.

体视学极值理论及其应用.

• 批准号: 06680285
• 负责人: TAKAHASHI Rinya
• 金额: $ 1.34万
• 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: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06680285/
• 关键词: extreme value theory; generalized gamma distribution; prediction; record-breaking; stereology; unfolding; Wicksell's corpuscle problem; 一般ガンマ分析; Wicksell問題; Wickse11問題

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.

主要研究了Wicksell粒子问题中的极值理论，即体视学中的经典问题，假设任意大小的球形粒子随机地散布在一个空间中，球体被一个剖切平面切割，我们只能观察到截面圆：1.证明了球体的大小分布和它的Wicksell变换属于同一类型的极值分布。一些相关结果也得到了证明。2.研究了给定体积内球体的最大尺寸预测问题。提出了几种可能的截面量测方法和相应的预测方法。通过仿真对预测方法的性能进行了研究。3.揭示了Wicksell小体问题不适定的原因。回顾了经典的记录展开方法，并对这些方法进行了改进，在分析记录统计的基础上，提出了一种统计模型和方法来预测未来的记录破坏。并将该方法应用于一些实际数据。

项目成果

Takahashi,R.: "The maximum size of the planar sections of random spheres and its application to metallurgy." Proceeding of In ternational Conference,statistics in Industry,Science and Technojogy. 197-202 (1994)

Takahashi,R.：“随机球体平面截面的最大尺寸及其在冶金中的应用。”

Takahashi, R.: "Domains of attraction of multivariate extreme value distributions." Journal of Research of the National Institute of Standards Technology. 99. 551-554 (1994)

Takahashi, R.：“多元极值分布的吸引力域。”

Takahashi, Rimya: "Asymptotic theory of extreme order statistics." Sugaku Expositions. 9. 53-67 (1996)

Takahashi, Rimya：“极端阶统计的渐近理论。”

Iiyama, Y.: "Power of record-breaking test (in Japanese)" Japanese Journal of Applied Statistics. 24. 13-26 (1995)

Iiyama, Y.：“破纪录测试的力量（日语）”日本应用统计杂志。

高橋倫也: "ウイクセル逆変換:ひとつの不適切問題" 応用統計学. 25・3(印刷中). (1996)

Tomoya Takahashi：“Wixel 逆变换：一个不适当的问题”应用统计 25, 3（出版中）。