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    A fast robust method for fitting gamma distributions

    Access Status
    Fulltext not available
    Authors
    Clarke, B.
    McKinnon, Peter
    Riley, G.
    Date
    2012
    Type
    Journal Article
    
    Metadata
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    Citation
    Clarke, B. and McKinnon, P. and Riley, G. 2012. A fast robust method for fitting gamma distributions. Statistical Papers. 53 (4): pp. 1001-1014.
    Source Title
    Statistical Papers
    DOI
    10.1007/s00362-011-0404-3
    ISSN
    0932-5026
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/29956
    Collection
    • Curtin Research Publications
    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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