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A fast robust method for fitting gamma distributions

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  • Brenton Clarke
  • Peter McKinnon
  • Geoff Riley

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. Copyright Springer-Verlag 2012

Suggested Citation

  • Brenton Clarke & Peter McKinnon & Geoff Riley, 2012. "A fast robust method for fitting gamma distributions," Statistical Papers, Springer, vol. 53(4), pages 1001-1014, November.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:1001-1014
    DOI: 10.1007/s00362-011-0404-3
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    References listed on IDEAS

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    1. Marazzi, A. & Ruffieux, C., 1999. "The truncated mean of an asymmetric distribution," Computational Statistics & Data Analysis, Elsevier, vol. 32(1), pages 79-100, November.
    2. Clarke, Brenton R., 1989. "An unbiased minimum distance estimator of the proportion parameter in a mixture of two normal distributions," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 275-281, February.
    3. B. Clarke & C. Heathcote, 1994. "Robust estimation ofk-component univariate normal mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 83-93, March.
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    Cited by:

    1. Muhammad Aslam Mohd Safari & Nurulkamal Masseran & Muhammad Hilmi Abdul Majid, 2020. "Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    2. Thieler, Anita M. & Fried, Roland & Rathjens, Jonathan, 2016. "RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i09).

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