Open Access
2024 Stereological determination of particle size distributions for similar convex bodies
Thomas van der Jagt, Geurt Jongbloed, Martina Vittorietti
Author Affiliations +
Electron. J. Statist. 18(1): 742-774 (2024). DOI: 10.1214/24-EJS2215


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 nonparametric estimator is proposed for this size distribution. The estimator is proven to be consistent and its performance is assessed in a simulation study.


We thank Kees Bos, Jilt Sietsma and Karo Sedighiani for fruitful discussions. We thank two reviewers and an associate editor for their constructive remarks.


Download Citation

Thomas van der Jagt. Geurt Jongbloed. Martina Vittorietti. "Stereological determination of particle size distributions for similar convex bodies." Electron. J. Statist. 18 (1) 742 - 774, 2024.


Received: 1 May 2023; Published: 2024
First available in Project Euclid: 23 February 2024

arXiv: 2305.02856
Digital Object Identifier: 10.1214/24-EJS2215

Primary: 60D05 , 62G05
Secondary: 60E10

Keywords: consistency , EM , iterative convex minorant , Mellin transform , Particle system , stereology

Vol.18 • No. 1 • 2024
Back to Top