Statistical Papers

, Volume 53, Issue 4, pp 1001–1014

A fast robust method for fitting gamma distributions

  • Brenton R. Clarke
  • Peter L. McKinnon
  • Geoff Riley
Regular Article

DOI: 10.1007/s00362-011-0404-3

Cite this article as:
Clarke, B.R., McKinnon, P.L. & Riley, G. Stat Papers (2012) 53: 1001. doi:10.1007/s00362-011-0404-3

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 L2 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 distributionsFréchet differentiabilityWeak continuityRobust estimationMinimum distance estimation

Mathematics Subject Classification (2000)

62F3562-07

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Brenton R. Clarke
    • 1
  • Peter L. McKinnon
    • 2
  • Geoff Riley
    • 3
  1. 1.Mathematics and Statistics, School of Chemical and Mathematical SciencesMurdoch UniversityMurdochAustralia
  2. 2.Mathematics and StatisticsCurtin UniversityBentleyAustralia
  3. 3.Technology Delivery GroupAlcoa World AluminaKwinanaAustralia