Statistical Papers

, Volume 60, Issue 3, pp 877–902 | Cite as

SB-robust estimation of mean direction for some new circular distributions

  • Arnab Kumar LahaEmail author
  • A. C. Pravida Raja
  • K. C. Mahesh
Regular Article


The most often used distribution for modelling directional data has been the circular normal (CN) (a.k.a. von-Mises) distribution. Recently Kato and Jones (K–J) introduced a family of distribution which includes the CN distribution as a special case. We study the SB-robustness of the circular mean functional (CMF) and show that the CMF is not SB-robust at the family of all symmetric Kato–Jones distributions but is SB-robust at sub-families with bounded parameters. It is also found to be SB-robust for certain sub-families of wrapped-t (WT) distributions, mixtures of K–J distributions and mixtures of K–J and WT distributions. The SB-robustness of the circular trimmed mean functional (CTMF) is also studied and it is found that the CTMF is SB-robust for larger sub-families of symmetric Kato–Jones distributions compared to that of CMF. The SB-robustness of the CMF for asymmetric families of distributions is studied and it is shown that CMF is SB-robust at a sub-family of asymmetric Kato–Jones distributions. The performance of CTM is compared with that of circular mean (CM) through extensive simulation. It is seen that CTM has better robustness properties than the CM both theoretically and practically. Some guidelines for choice of trimming proportion for CTM is given.


Circular data Circular trimmed mean Kato–Jones distribution Measures of dispersion SB-robustness Wrapped-t distribution 



The authors express gratitude to the anonymous referees and the editor for their valuable comments which led to substantial improvement of the article.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Arnab Kumar Laha
    • 1
    Email author
  • A. C. Pravida Raja
    • 1
  • K. C. Mahesh
    • 2
  1. 1.Indian Institute of Management, AhmedabadAhmedabadIndia
  2. 2.Institute of ManagementNirma UniversityAhmedabadIndia

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