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Estimation of Fibre Length Distributions from Fibre Endpoints

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  • Malte Kuhlmann
  • Claudia Redenbach

Abstract

type="main" xml:id="sjos12148-abs-0001"> 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.

Suggested Citation

  • Malte Kuhlmann & Claudia Redenbach, 2015. "Estimation of Fibre Length Distributions from Fibre Endpoints," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1010-1022, December.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:1010-1022
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    File URL: http://hdl.handle.net/10.1111/sjos.12148
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    References listed on IDEAS

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    1. Ingrid Svensson & Sara Sjöstedt‐De Luna & Lennart Bondesson, 2006. "Estimation of Wood Fibre Length Distributions from Censored Data through an EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 503-522, September.
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    Cited by:

    1. Patricia Alonso Ruiz & Evgeny Spodarev, 2018. "Entropy-based Inhomogeneity Detection in Fiber Materials," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1223-1239, December.

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