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Sine-skewed circular distributions

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Abstract

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.

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Authors and Affiliations

  1. School of Fundamental Science and Technology, Keio University, Yokohama, Japan

    Toshihiro Abe

  2. Department of Mathematics, Escuela Politécnica, University of Extremadura, Cáceres, Spain

    Arthur Pewsey

Authors
  1. Toshihiro Abe
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  2. Arthur Pewsey
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Correspondence to Toshihiro Abe.

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Abe, T., Pewsey, A. Sine-skewed circular distributions. Stat Papers 52, 683–707 (2011). https://doi.org/10.1007/s00362-009-0277-x

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  • DOI: https://doi.org/10.1007/s00362-009-0277-x

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