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Biometrika 1971 58(3):483-490; doi:10.1093/biomet/58.3.483
© 1971 by Biometrika Trust
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Estimating functionals of particle size distributions

G. S. WATSON

Princeton University

Data consisting of the intersections of a planar or linear probe with a field of spheres, with a diameter distribution G(x), is often used to estimate linear functionals or their ratios. It is shown that distribution-free estimators may be poor and that their distribution, even in large samples, depends on knowledge of G for small x that may be unobtainable. The parametric approach is arduous and not robust against errors in the lower tail. It seems that this experimental method should be avoided when there is a practicable alternative.

Key Words: Particle size distribution • Estimation of functionals of distributions • Biased sampling of spheres • Metallurgical applications • Geometrical probability • Method of substitution • Limit theorems • Distribution-free estimation • Spheres • Stereology


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