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An adjusted boxplot for skewed distributions

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  • Hubert, M.
  • Vandervieren, E.
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/csda

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    References

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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. Carling, Kenneth, 2000. "Resistant outlier rules and the non-Gaussian case," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 249-258, May.
    3. 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.
    4. 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.
    5. Schwertman, Neil C. & de Silva, Rapti, 2007. "Identifying outliers with sequential fences," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3800-3810, May.
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    Cited by:
    1. Olivia D'Aoust & Olivier Sterck & Philip Verwimp, 2013. "Buying Peace: The Mirage of Demobilizing Rebels," Working Papers ECARES ECARES 2013-22, ULB -- Universite Libre de Bruxelles.
    2. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Zeller, Camila Borelli, 2014. "Multivariate measurement error models using finite mixtures of skew-Student t distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 179-198.
    3. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    4. M. Hubert & P. Rousseeuw & K. Vakili, 2014. "Shape bias of robust covariance estimators: an empirical study," Statistical Papers, Springer, vol. 55(1), pages 15-28, February.
    5. 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.
    6. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    7. Mia Hubert & Irène Gijbels & Dina Vanpaemel, 2013. "Reducing the mean squared error of quantile-based estimators by smoothing," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 448-465, September.
    8. Asuman Turkmen & Nedret Billor, 2013. "Partial least squares classification for high dimensional data using the PCOUT algorithm," Computational Statistics, Springer, vol. 28(2), pages 771-788, April.
    9. Robert Finger, 2010. "Review of ‘Robustbase’ software for R," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1205-1210, November/.
    10. Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.

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