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Symmetric circular models through duplication and cosine perturbation

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  • Abe, Toshihiro
  • Pewsey, Arthur

Abstract

Models for circular data displaying two diametrically opposed modes are considered. A general construction which can be used to generate such models, founded upon doubling the argument of a base symmetric unimodal distribution and cosine perturbation, is proposed. Fundamental properties of the resulting models are described, as are those of a particularly flexible family of distributions and three of its submodels. Parameter estimation via the method of moments and maximum likelihood is discussed, and a likelihood-ratio test for antipodal symmetry developed. The application of the proposed models and inferential methods is illustrated using two animal orientation data sets.

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  • Abe, Toshihiro & Pewsey, Arthur, 2011. "Symmetric circular models through duplication and cosine perturbation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3271-3282, December.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3271-3282
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    References listed on IDEAS

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    1. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    2. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    3. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    4. Arthur Pewsey, 2004. "Testing for Circular Reflective Symmetry about a Known Median Axis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(5), pages 575-585.
    5. Jones, M.C. & Pewsey, Arthur, 2005. "A Family of Symmetric Distributions on the Circle," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1422-1428, December.
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    1. Oliveira, M. & Crujeiras, R.M. & Rodríguez-Casal, A., 2012. "A plug-in rule for bandwidth selection in circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3898-3908.
    2. Nuñez-Antonio, Gabriel & Gutiérrez-Peña, Eduardo, 2014. "A Bayesian model for longitudinal circular data based on the projected normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 506-519.

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