Models for Axial Data

  • Barry C. Arnold
  • Ashis SenGupta


A variety of models have been proposed to accommodate data involving directional vectors in two-dimensions, with no identified start or end point. By convention such directions are represented by points in the interval (0,π). Data of this kind is called axial data. A survey of symmetric and asymmetric models for axial data is provided here. In addition, for certain models, parametric inference issues are addressed. In some cases, bivariate and multivariate extensions are readily envisioned.


Environ Ecol Stat Cauchy Distribution Axial Distribution Axial Variable Circular Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Arnold B, SenGupta A (2006) Probability distributions and statistical inference for axial data. Environ Ecol Stat 12:271–285CrossRefMathSciNetGoogle Scholar
  2. 2.
    Arnold B, SenGupta A (2009) Flexible bivariate circular models. In: Advances in multivariate statistical methods. World Scientific, SingaporeGoogle Scholar
  3. 3.
    Arnold B, Strauss D (1991) Bivariate distributions with conditionals in prescribed exponential families. J R Stat Soc Series B 53:365–375MATHMathSciNetGoogle Scholar
  4. 4.
    Azzalini A (2005) The skew-normal distribution and related multivariate families. Scand J Stat 32:159–200MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jammalamadaka SR, Kozubowski T (2004) New families of wrapped distributions for modeling skew circular data. Commun Stat Theory Methods 33(9):2059–2074MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jammalamadaka SR, SenGupta A (2001) Topics in circular statistics. World Scientific, SingaporeMATHCrossRefGoogle Scholar
  7. 7.
    Jones MC, Pewsey A (2005) A family of symmetric distributions on the circle. J Am Stat Assoc 100:1422–1428MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Mardia KV, Jupp PE (2000) Directional statistics. Wiley, New YorkMATHGoogle Scholar
  9. 9.
    Pewsey A (2006) Modeling asymmetrically distributed circular data using the wrapped skew-normal distribution. Environ Ecol Stat 13:257–269CrossRefMathSciNetGoogle Scholar
  10. 10.
    Umbach D, Jammalamadaka SR (2009) Building asymmetry into circular distributions. Stat Probab Lett 79:659–663MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of CaliforniaRiversideUSA

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