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Title: Stereology of extremes; size of spheroids (English)
Author: Hlubinka, Daniel
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 128
Issue: 4
Year: 2003
Pages: 419-438
Summary lang: English
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Category: math
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Summary: The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of appropriate distribution functions and its results are employed for the estimation of the spheroid size. Examples covering families of Gamma, Pareto and Weibull distributions are provided. A short discussion of maximum likelihood estimators of the normalizing constants is also included. (English)
Keyword: sample extremes
Keyword: domain of attraction
Keyword: normalizing constants
Keyword: FGM system of distributions
MSC: 60G70
MSC: 62G32
MSC: 62P30
idZBL: Zbl 1053.60053
idMR: MR2032479
DOI: 10.21136/MB.2003.134007
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Date available: 2009-09-24T22:11:36Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/134007
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