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Simple construction of a toroidal distribution from independent circular distributions

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  • Imoto, Tomoaki
  • Abe, Toshihiro

Abstract

In this paper, we propose a new method for constructing a toroidal distribution from independent circular distributions by specifying marginal distributions. The constructed probability density function is expressed without additional normalizing constants, and its conditional distributions belong to the family of sine-skewed circular distributions. The simple expressions for trigonometric moments, especially for correlation measures, help characterize the proposed model. Maximum likelihood estimation is computationally tractable, and the correlation parameter is orthogonal to the location and concentration parameters when the marginal distributions are symmetric. Two illustrative applications are shown comparing genome structures between paired bacteria.

Suggested Citation

  • Imoto, Tomoaki & Abe, Toshihiro, 2021. "Simple construction of a toroidal distribution from independent circular distributions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000774
    DOI: 10.1016/j.jmva.2021.104799
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    References listed on IDEAS

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    1. Shogo Kato & Arthur Pewsey, 2015. "A Möbius transformation-induced distribution on the torus," Biometrika, Biometrika Trust, vol. 102(2), pages 359-370.
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    3. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
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    5. Abe, Toshihiro & Ley, Christophe, 2017. "A tractable, parsimonious and flexible model for cylindrical data, with applications," Econometrics and Statistics, Elsevier, vol. 4(C), pages 91-104.
    6. Shogo Kato & M. C. Jones, 2015. "A tractable and interpretable four-parameter family of unimodal distributions on the circle," Biometrika, Biometrika Trust, vol. 102(1), pages 181-190.
    7. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
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