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Stereological estimation of particle size distributions

Part of: Inference from stochastic processes Nonparametric inference Numerical approximation and computational geometry Applications

Published online by Cambridge University Press:  01 July 2016

Shigeru Mase
Shigeru Mase*
Affiliation:
Hiroshima University
*
* Postal address: Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima City, 724 Japan.
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Abstract

The corpuscle problem of Wicksell is discussed. We give a numerical quadrature of Gauss–Chebyshev type for Wicksell's integral equation which combines a size distribution of discs on a sectional plane with that of spheres. We also give an estimation procedure of three-dimensional size distributions based on this quadrature and examine its theoretical properties. In practice, we need a smoothing technique for empirical distribution functions before applying this estimator. Simulation results are given. Our idea also is applied to the thick section case and an analysis of microscopic data is given.

Keywords

WICKSELL'S EQUATIONSTEREOLOGYGAUSS–CHEBYSHEV QUADRATURESIZEDISTRIBUTIONSECTIONAL PLANECORPUSCLE PROBLEMSMOOTHING

MSC classification

Primary: 62G07: Density estimation
Secondary: 62P10: Applications to biology and medical sciences 62G20: Asymptotic properties 62M30: Spatial processes 65D30: Numerical integration
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 350 - 366
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain, on 21–24 September 1993.

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