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Boxplot for circular variables

Author

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  • 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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    File URL: http://hdl.handle.net/10.1007/s00180-011-0261-5
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    References listed on IDEAS

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    1. 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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