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An adjusted boxplot for skewed distributions


  • Hubert, M.
  • Vandervieren, E.


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.

Suggested Citation

  • Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5186-5201

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    References listed on IDEAS

    1. Carling, Kenneth, 2000. "Resistant outlier rules and the non-Gaussian case," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 249-258, May.
    2. Brys, Guy & Hubert, Mia & Struyf, Anja, 2006. "Robust measures of tail weight," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 733-759, February.
    3. Schwertman, Neil C. & de Silva, Rapti, 2007. "Identifying outliers with sequential fences," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3800-3810, May.
    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. & 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.
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    Cited by:

    1. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    2. 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.
    3. Jeremias Leão & Francisco Cysneiros & Helton Saulo & N. Balakrishnan, 2016. "Constrained test in linear models with multivariate power exponential distribution," Computational Statistics, Springer, vol. 31(4), pages 1569-1592, December.
    4. Vincenzo Verardi, 2013. "Semiparametric regression in Stata," United Kingdom Stata Users' Group Meetings 2013 14, Stata Users Group.
    5. repec:spr:stpapr:v:59:y:2018:i:2:d:10.1007_s00362-016-0774-7 is not listed on IDEAS
    6. 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.
    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;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 448-465, September.
    8. Boente, Graciela & Vahnovan, Alejandra, 2017. "Robust estimators in semi-functional partial linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 59-84.
    9. 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.
    10. Robert Finger, 2010. "Review of ‘Robustbase’ software for R," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1205-1210, November/.
    11. repec:spr:alstar:v:101:y:2017:i:3:d:10.1007_s10182-017-0291-6 is not listed on IDEAS
    12. 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.
    13. repec:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0269-3 is not listed on IDEAS
    14. Bruffaerts, Christopher & Verardi, Vincenzo & Vermandele, Catherine, 2014. "A generalized boxplot for skewed and heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 110-117.
    15. Václav Plevka & Pieter Segaert & Chris M. J. Tampère & Mia Hubert, 2016. "Analysis of travel activity determinants using robust statistics," Transportation, Springer, vol. 43(6), pages 979-996, November.
    16. 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.
    17. Finger, Robert, 2012. "Biases in Farm-Level Yield Risk Analysis due to Data Aggregation," Journal of International Agricultural Trade and Development, Journal of International Agricultural Trade and Development, vol. 61(1).
    18. 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.
    19. 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.
    20. 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.
    21. repec:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0073-4 is not listed on IDEAS
    22. Bourguignon, Marcelo & Saulo, Helton & Fernandez, Rodrigo Nobre, 2016. "A new Pareto-type distribution with applications in reliability and income data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 166-175.

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