Stereology of Extremes; Bivariate Models and Computation

Viktor Beneš (), Karel Bodlák () and Daniel Hlubinka ()
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Viktor Beneš: Charles University
Karel Bodlák: Charles University
Daniel Hlubinka: Charles University

Methodology and Computing in Applied Probability, 2003, vol. 5, issue 3, 289-308

Abstract: Abstract The extremal shape factor of spheroidal particles is studied in the stereological context using the extreme value theory. The domain of attraction is invariant with respect to the transformation between spatial characteristics and planar sections characteristics. It is shown that for the Farlie-Gumbel-Morgenstern bivariate distribution of size and shape factor one can estimate the normalizing constants of shape factor conditioned by unknown particle size. The theoretical solution is followed by a detailed simulation study which demonstrates the use of estimation techniques developed. The method is useful for engineering applications in materials science, where microstructural extremes correlate with the properties of materials.

Keywords: sample extremes; domain of attraction; normalizing constants; FGM distribution (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1026283103180

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