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An adjusted boxplot for skewed distributions

  • Hubert, M.
  • Vandervieren, E.
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    The boxplot is a very popular graphical tool for visualizing the distribution of continuous unimodal data. It shows information about the location, spread, skewness as well as the tails of the data. However, when the data are skewed, usually many points exceed the whiskers and are often erroneously declared as outliers. An adjustment of the boxplot is presented that includes a robust measure of skewness in the determination of the whiskers. This results in a more accurate representation of the data and of possible outliers. Consequently, this adjusted boxplot can also be used as a fast and automatic outlier detection tool without making any parametric assumption about the distribution of the bulk of the data. Several examples and simulation results show the advantages of this new procedure.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4R5VYHX-1/2/b3b3d34259d7e9047640873d9b0b0a2e
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 52 (2008)
    Issue (Month): 12 (August)
    Pages: 5186-5201

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    Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5186-5201
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Brys, Guy & Hubert, Mia & Struyf, Anja, 2006. "Robust measures of tail weight," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 733-759, February.
    2. Schwertman, Neil C. & de Silva, Rapti, 2007. "Identifying outliers with sequential fences," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3800-3810, May.
    3. Carling, Kenneth, 2000. "Resistant outlier rules and the non-Gaussian case," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 249-258, May.
    4. Schwertman, Neil C. & Owens, Margaret Ann & Adnan, Robiah, 2004. "A simple more general boxplot method for identifying outliers," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 165-174, August.
    5. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
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