Kernel estimators are proposed for estimating the cumulative distribution functions and the probability density functions of several quantities of interest in a stereological oriented cylinder model. This oriented cylinder model was developed to represent anisotropic microstructural features in materials. The asymptotic properties of these estimators are studied, and the estimators are applied to two banded dual phase steel microstructures. The estimation method is quite general and can also be applied to distributions of other univariate quantities of interest.

中文翻译：

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定向圆柱模型中尺寸分布的平滑估计

提出了核估计器，用于估计面向立体的圆柱体模型中多个感兴趣量的累积分布函数和概率密度函数。开发了这种定向圆柱体模型来表示材料中的各向异性微观结构特征。研究了这些估计量的渐近性质，并将这些估计量应用于两个带状双相钢微结构。估计方法非常通用，也可以应用于其他单变量关注点的分布。