IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v53y2012i4p1001-1014.html
   My bibliography  Save this article

A fast robust method for fitting gamma distributions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-011-0404-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-011-0404-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brenton R. Clarke & Thomas Davidson & Robert Hammarstrand, 2017. "A comparison of the $$L_2$$ L 2 minimum distance estimator and the EM-algorithm when fitting $${\varvec{{k}}}$$ k -component univariate normal mixtures," Statistical Papers, Springer, vol. 58(4), pages 1247-1266, December.
    2. Kim, Byungsoo & Lee, Sangyeol, 2013. "Robust estimation for the covariance matrix of multivariate time series based on normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 125-140.
    3. Karlis, Dimitris & Xekalaki, Evdokia, 1998. "Minimum Hellinger distance estimation for Poisson mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 81-103, November.
    4. Clarke, Brenton R. & Futschik, Andreas, 2007. "On the convergence of Newton's method when estimating higher dimensional parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 916-931, May.
    5. Brazauskas, Vytaras, 2003. "Influence functions of empirical nonparametric estimators of net reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 115-133, February.
    6. Brigitte Dormont & Hélène Huber, 2006. "Ageing and changes in medical practices : reassessing theinfluence of demography," Post-Print halshs-00274723, HAL.
    7. Marazzi, A., 2002. "Bootstrap tests for robust means of asymmetric distributions with unequal shapes," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 503-528, June.
    8. Anthony Ebert & Ritabrata Dutta & Kerrie Mengersen & Antonietta Mira & Fabrizio Ruggeri & Paul Wu, 2021. "Likelihood‐free parameter estimation for dynamic queueing networks: Case study of passenger flow in an international airport terminal," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 770-792, June.
    9. 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.
    10. Peter Ruckdeschel & Nataliya Horbenko, 2012. "Yet another breakdown point notion: EFSBP," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1025-1047, November.
    11. Borislava Mihaylova & Andrew Briggs & Anthony O'Hagan & Simon G. Thompson, 2011. "Review of statistical methods for analysing healthcare resources and costs," Health Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 897-916, August.
    12. Taewook Lee & Sangyeol Lee, 2009. "Consistency of minimizing a penalized density power divergence estimator for mixing distribution," Statistical Papers, Springer, vol. 50(1), pages 67-80, January.
    13. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:1001-1014. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.