A fast robust method for fitting gamma distributions

作者：Clarke Brenton R^*; McKinnon Peter L; Riley Geoff

来源：Statistical Papers, 2012, 53(4): 1001-1014.

DOI：10.1007/s00362-011-0404-3

• Gamma distributions
• Frechet differentiability
• Weak continuity
• Robust estimation
• Minimum distance estimation

The art of fitting gamma distributions robustly is described. In particular we compare methods of fitting via minimizing a Cram,r 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 Fr,chet 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 Cram,r Von Mises distance is both efficacious in terms of efficiency and robustness as well as being easily implemented. Here gamma distributions arise naturally for %26quot;in control%26quot; 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.

• 出版日期2012-11