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A fast robust method for fitting gamma distributions

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Abstract

The art of fitting gamma distributions robustly is described. In particular we compare methods of fitting via minimizing a Cramér Von Mises distance, an L 2 minimum distance estimator, and fitting a B-optimal M-estimator. After a brief prelude on robust estimation explaining the merits in terms of weak continuity and Fréchet differentiability of all the aforesaid estimators from an asymptotic point of view, a comparison is drawn with classical estimation and fitting. In summary, we give a practical example where minimizing a Cramér Von Mises distance is both efficacious in terms of efficiency and robustness as well as being easily implemented. Here gamma distributions arise naturally for “in control” representation indicators from measurements of spectra when using fourier transform infrared (FTIR) spectroscopy. However, estimating the in-control parameters for these distributions is often difficult, due to the occasional occurrence of outliers.

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Authors and Affiliations

  1. Mathematics and Statistics, School of Chemical and Mathematical Sciences, Murdoch University, 6150, Murdoch, WA, Australia

    Brenton R. Clarke

  2. Mathematics and Statistics, Curtin University, Bentley, WA, 6102, Australia

    Peter L. McKinnon

  3. Technology Delivery Group, Alcoa World Alumina, Kwinana, WA, 6966, Australia

    Geoff Riley

Authors
  1. Brenton R. Clarke
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  2. Peter L. McKinnon
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  3. Geoff Riley
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Correspondence to Brenton R. Clarke.

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Clarke, B.R., McKinnon, P.L. & Riley, G. A fast robust method for fitting gamma distributions. Stat Papers 53, 1001–1014 (2012). https://doi.org/10.1007/s00362-011-0404-3

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  • DOI: https://doi.org/10.1007/s00362-011-0404-3

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