Stereological determination of particle size distributions for similar convex bodies

Journal Article (2024)
Author(s)

T.F.W. van der Jagt (TU Delft - Statistics)

G Jongbloed (TU Delft - Statistics)

Martina Vittorietti (Università degli Studi di Palermo, TU Delft - Statistics)

Research Group
Statistics
Copyright
© 2024 T.F.W. van der Jagt, G. Jongbloed, M. Vittorietti
DOI related publication
https://doi.org/10.1214/24-EJS2215
More Info
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Publication Year
2024
Language
English
Copyright
© 2024 T.F.W. van der Jagt, G. Jongbloed, M. Vittorietti
Research Group
Statistics
Issue number
1
Volume number
18
Pages (from-to)
742-774
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Abstract

Consider an opaque medium that contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a planar section of the medium we obtain a sample of observed 2D section profile areas of the intersected particles. In this paper, the distribution of interest is the underlying 3D particle size distribution for which an identifiability result is obtained. Moreover, a non-parametric estimator is proposed for this size distribution. The estimator is proven to be consistent and its performance is assessed in a simulation study.