Existence and approximation of densities of chord length- and cross section area distributions

Journal Article (2023)
Author(s)

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

G Jongbloed (TU Delft - Statistics)

Martina Vittorietti (Università degli Studi di Palermo)

Research Group
Statistics
Copyright
© 2023 T.F.W. van der Jagt, G. Jongbloed, M. Vittorietti
More Info
expand_more
Publication Year
2023
Language
English
Copyright
© 2023 T.F.W. van der Jagt, G. Jongbloed, M. Vittorietti
Research Group
Statistics
Pages (from-to)
171-184
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

In various stereological problems ann-dimensional convex body is intersected with an(n−1)-dimensionalIsotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associatedwith the(n−1)-dimensional volume of such a random section is studied. This distribution is also knownas chord length distribution and cross section area distribution in the planar and spatial case respectively.For various classes of convex bodies it is shown that these distribution functions are absolutely continuouswith respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating thecorresponding probability density functions.