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Estimation of Fibre Length Distributions from Fibre Endpoints
Author(s) -
Kuhlmann Malte,
Redenbach Claudia
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12148
Subject(s) - estimator , mathematics , moment (physics) , mean squared error , realization (probability) , stein's unbiased risk estimate , point process , heuristic , bias of an estimator , algorithm , statistics , minimum variance unbiased estimator , mathematical optimization , physics , classical mechanics
Estimating the fibre length distribution in composite materials is of practical relevance in materials science. We propose an estimator for the fibre length distribution using the point process of fibre endpoints as input. Assuming that this point process is a realization of a Neyman–Scott process, we use results for the reduced second moment measure to derive a consistent and unbiased estimator for the fibre length distribution. We introduce various versions of the estimator taking anisotropy or errors in the observation into account. The estimator is evaluated using a heuristic for its mean squared error as well as a simulation study. Finally, the estimator is applied to the fibre endpoint process extracted from a tomographic image of a glass fibre composite.