Computational Statistics

, Volume 27, Issue 3, pp 381–392 | Cite as

Boxplot for circular variables

  • Ali H. Abuzaid
  • Ibrahim B. Mohamed
  • Abdul G. Hussin
Original Paper

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.

Keywords

Circular boxplot Boxplot Resistant constant Outlier Overlapping 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abuzaid AH, Hussin AG, Mohamed IB (2008) Identifying single outlier in linear circular regression model based on circular distance. J Appl Probab Stat 3(1): 107–117MathSciNetMATHGoogle Scholar
  2. Abuzaid AH, Mohamed IB, Hussin AG (2009) A new test of discordancy in circular data. Commun Stat Simul Comput 38(4): 682–691MathSciNetMATHCrossRefGoogle Scholar
  3. Barnett V, Lewis T (1978) Outliers in statistical data. Wiley, New YorkMATHGoogle Scholar
  4. Collett D (1980) Outliers in circular data. Appl Stat 29(1): 50–57MATHCrossRefGoogle Scholar
  5. David HA (1970) Order statistics. Wiley, New YorkMATHGoogle Scholar
  6. Ferguson DE, Landerth HF, Mckeown JP (1967) Sun compass orientation of the northern cricket frog. Acris Crepitans Anim Behav 15: 45–53Google Scholar
  7. Fisher NI (1993) Statistical analysis of circular data. Cambridge University Press, LondonMATHCrossRefGoogle Scholar
  8. Fox J (1997) Applied regression analysis, linear models, and related models. Sage Publication, SingaporeGoogle Scholar
  9. Graedel TE (1977) The wind boxplot: an improved wind rose. J Appl Meteorol 16: 448–450CrossRefGoogle Scholar
  10. Hoaglin DC, Iglewicz B, Tukey JW (1986) Performance of some resistant rules for outlier labeling. J Am Stat Assoc 81(396): 991–999MathSciNetMATHCrossRefGoogle Scholar
  11. Hussin AG, Fieller NRJ, Stillman EC (2004) Linear regression for circular variables with application to directional data. J Appl Sci Technol 8(1&2): 1–6Google Scholar
  12. Ingelfinger JA, Mosteller F, Thibodeau LA, Ware JH (1983) Biostatistics in clinical medicine. Macmillan, New YorkGoogle Scholar
  13. Jammalamadaka SR, SenGupta A (2001) Topics in circular statistics. World Scientific Press, SingaporeMATHGoogle Scholar
  14. Jammalamadaka SR, SenGupta A (2003) Linear statistical models: an integrated approach. World Scientific Press, SingaporeGoogle Scholar
  15. Mardia KV (1972) Statistics of directional data. Academic Press, LondonMATHGoogle Scholar
  16. Mardia KV (1975) Statistics of directional data. J R Stat Soc B 37: 349–393MathSciNetMATHGoogle Scholar
  17. Mardia VK, Jupp PE (2000) Directional data 2nd. Wiley, LondonGoogle Scholar
  18. Sim CH, Gan FF, Chang TC (2005) Outlier labeling with boxplot procedures. J Am Stat Assoc 100(470): 642–652MathSciNetMATHCrossRefGoogle Scholar
  19. Tukey JW (1977) Exploratory data analysis. Addison-Wesley, ReadingMATHGoogle Scholar
  20. Wehrly T, Shine EP (1981) Influence curves of estimates for directional data. Biometrika 68: 334–335MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Ali H. Abuzaid
    • 1
  • Ibrahim B. Mohamed
    • 1
  • Abdul G. Hussin
    • 2
  1. 1.Institute of Mathematical SciencesUniversity of MalayaKuala LumpurMalaysia
  2. 2.Center for Foundation Studies in ScienceUniversity of MalayaKuala LumpurMalaysia

Personalised recommendations