Abstract
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.
Highlights
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
The asymptotic properties of these estimators are studied, and the estimators are applied to two banded dual phase steel microstructures
The so-called Wicksell problem introduced in Wicksell (1925) is a classical inverse problem in statistics
Summary
The so-called Wicksell problem introduced in Wicksell (1925) is a classical inverse problem in statistics. A postmortem examination of spleens containing approximately spherical tumors was performed. Based on cross sections of the spleens (showing circular profiles of the tumors), the aim was to estimate the distribution of tumor sizes based on the observed circle radii. Wicksell’s problem is a typical example of a stereological problem, where one aims to infer ‘three-dimensional properties’ from ‘two-dimensional information’. Within the field of anatomy, and in materials science and astronomy, this type of problem
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