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A Möbius transformation-induced distribution on the torus

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  • Shogo Kato
  • Arthur Pewsey

Abstract

We propose a five-parameter bivariate wrapped Cauchy distribution as a unimodal model for toroidal data. It is highly tractable, displays numerous desirable properties, including marginal and conditional distributions that are all wrapped Cauchy, and arises as an appealing submodel of a six-parameter distribution obtained by applying Möbius transformation to a pre-existing bivariate circular model. Method of moments and maximum likelihood estimation of its parameters are fast, and tests for independence and goodness-of-fit are available. An analysis involving dihedral angles of the proteinogenic amino acid Tyrosine illustrates the distribution’s application. A Markov process for circular data is also explored.

Suggested Citation

  • Shogo Kato & Arthur Pewsey, 2015. "A Möbius transformation-induced distribution on the torus," Biometrika, Biometrika Trust, vol. 102(2), pages 359-370.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:2:p:359-370.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv003
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    Cited by:

    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. Imoto, Tomoaki & Abe, Toshihiro, 2021. "Simple construction of a toroidal distribution from independent circular distributions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    3. Masanobu Taniguchi & Shogo Kato & Hiroaki Ogata & Arthur Pewsey, 2020. "Models for circular data from time series spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 808-829, November.
    4. Ghosh, Malay & Zhong, Xiaolong & SenGupta, Ashis & Zhang, Ruoyang, 2019. "Non-subjective priors for wrapped Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 90-97.

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