Statistical Papers

, Volume 52, Issue 3, pp 683–707

Sine-skewed circular distributions

Regular Article

DOI: 10.1007/s00362-009-0277-x

Cite this article as:
Abe, T. & Pewsey, A. Stat Papers (2011) 52: 683. doi:10.1007/s00362-009-0277-x


In this paper, we consider skew-symmetric circular distributions generated by perturbation of a symmetric circular distribution. The main focus of the paper, the sine-skewed family of distributions, is a special case of the construction due to Umbach and Jammalamadaka (Stat Probab Lett 79:659–663, 2009). Very general results are provided for the properties of any such distribution, and the sine-skewed Jones–Pewsey distribution is introduced as a particularly flexible model of this type. We study its properties as well as those of three of its special cases. General results are also provided for maximum likelihood estimation of the parameters of any sine-skewed distribution. The developed models and methods of inference are applied in analyses of three circular data sets. Two of them shed new light on previously published analyses.


Circular statistics Finite mixtures Jones–Pewsey family Likelihood-based inference Modality Trigonometric moments 

Mathematics Subject Classification (2000)

60E05 62H11 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.School of Fundamental Science and TechnologyKeio UniversityYokohamaJapan
  2. 2.Department of Mathematics, Escuela PolitécnicaUniversity of ExtremaduraCáceresSpain