Regular Article

Statistical Papers

, Volume 53, Issue 4, pp 1001-1014

A fast robust method for fitting gamma distributions

  • Brenton R. ClarkeAffiliated withMathematics and Statistics, School of Chemical and Mathematical Sciences, Murdoch University Email author 
  • , Peter L. McKinnonAffiliated withMathematics and Statistics, Curtin University
  • , Geoff RileyAffiliated withTechnology Delivery Group, Alcoa World Alumina

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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.

Keywords

Gamma distributions Fréchet differentiability Weak continuity Robust estimation Minimum distance estimation

Mathematics Subject Classification (2000)

62F35 62-07