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Boxplot for circular variables

Author

Listed:
  • Ali Abuzaid
  • Ibrahim Mohamed
  • Abdul Hussin

Abstract

A boxplot is a simple and flexible graphical tool which has been widely used in exploratory data analysis. One of its main applications is to identify extreme values and outliers in a univariate data set. While the boxplot is useful for a real line data set, it is not suitable for a circular data set due to the fact that there is no natural ordering of circular observations. In this paper, we propose a boxplot version for a circular data set, called the circular boxplot. The problem of finding the appropriate circular boxplot criterion of the form ν × CIQR, where CIQR is the circular interquartile range and ν is the resistant constant, is investigated through a simulation study. As might be expected, we find that the choice of ν depends on the value of the concentration parameter κ. Another simulation study is done to investigate the performance of the circular boxplot in detecting a single outlier. Our results show that the circular boxplot performs better when both the value of κ and the sample size are larger. We develop a visual display for the circular boxplot in S-Plus and illustrate its application using two real circular data sets. Copyright Springer-Verlag 2012

Suggested Citation

  • Ali Abuzaid & Ibrahim Mohamed & Abdul Hussin, 2012. "Boxplot for circular variables," Computational Statistics, Springer, vol. 27(3), pages 381-392, September.
    • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:381-392
    DOI: 10.1007/s00180-011-0261-5
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    References listed on IDEAS

    as
    1. D. Collett, 1980. "Outliers in Circular Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 50-57, March.
    2. Sim, C.H. & Gan, F.F. & Chang, T.C., 2005. "Outlier Labeling With Boxplot Procedures," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 642-652, June.
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    Cited by:

    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. Abuzaid Ali H., 2020. "Detection of Outliers in Univariate Circular Data by Means of the Outlier Local Factor (LOF)," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 39-51, September.
    3. Ali H. Abuzaid, 2020. "Detection of Outliers in Univariate Circular Data by Means of the Outlier Local Factor (LOF)," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 39-51, September.
    4. Najla M. Qarmalah & Jochen Einbeck & Frank P. A. Coolen, 2018. "k-Boxplots for mixture data," Statistical Papers, Springer, vol. 59(2), pages 513-528, June.

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