Prediction in Wicksell's Corpuscle Problem.

威克塞尔的皮细胞问题的预测。

• 批准号: 13680373
• 负责人: TAKAHASHI Rinya
• 金额: $ 0.83万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13680373/
• 关键词: extreme value theory; Gumbel distribution; prediction; quantile; return level; r largest observations; stereology; ウィクセル小球問題; グンベル分布; 指数分布; 一般ガンマ分布; シミュレーション

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.

1.高强度钢的疲劳强度与钢中最大应力区非金属夹杂物的最大尺寸密切相关。因此，有必要预测夹杂物的最大尺寸的基础上测量的尺寸数据在显微镜下观察领域的平面部分的试样。一个统计问题是从Wicksell变换的观测值中推断不可测极值的分布。2.在Wicksell粒子问题中，随机球的最大尺寸是由球的平面截面的圆的尺寸分布来预测的。如果球的大圆的面积具有指数尾部，则应用简单的预测方法。通过仿真对这些方法的性能进行了评估，并将其应用于球墨铸铁中石墨球尺寸的数据集。3.假设在n个单位区域或区间内观察到较大的值。为了估计小上尾概率的分位数，使用n个数据集的r个最大值。最大似然估计相对于r=1的渐近效率见表。沿着讨论分析了腐蚀产生的小坑深度。

项目成果

Takahashi, Rinya: "Metal fatigue, Wicksell transform and extreme values"Appl.Stochastic Models Bus.Ind.. Vol.18. 301-312 (2002)

Takahashi, Rinya：“金属疲劳、Wicksell 变换和极值”Appl.Stochastic Models Bus.Ind.. Vol.18。

高橋 倫也: "上位r個の観測地に基づく確立点の推定"統計数理. 第52巻・第1号. (2004)

Tomoya Takahashi：“基于前 r 个观测点的概率点估计”《统计数学》第 52 卷，第 1 期（2004 年）。

Takahashi, R., Sibuya, M.: "Maximum size prediction in Wicksell's Corpuscle problem for the exponential tail date"Extremes. Vol.5. 55-70 (2002)

Takahashi, R.、Sibuya, M.：“指数尾部日期的维克塞尔小体问题中的最大尺寸预测”极端。

Sibuya, M., Hanayama, N.: "Estimation of human longevity distribution Based on tabulated statistics.(in Japanese)"Proseedings of the Institute of Statistical Mathematics. Vol.52(To appear). (2004)

Sibuya, M., Hanayama, N.：“基于表格统计的人类寿命分布估计。（日语）”统计数学研究所的论文集。

Rinya Takahashi: "Metal fatigue, Wicksell transform and extreme values"Applied Stochastic Models in Business and Industry. 18・3. 301-312 (2002)

Rinya Takahashi：“金属疲劳、Wicksell 变换和极值”《商业和工业中的应用随机模型》18・3（2002 年）。