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Bayesian tests of symmetry for the generalized Von Mises distribution

Author

Listed:
  • Sara Salvador

    (University of Bern)

  • Riccardo Gatto

    (University of Bern)

Abstract

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric, unimodal or bimodal. A characterization of axial symmetry is provided and taken as null hypothesis for one of the proposed Bayesian tests. The Bayesian tests are obtained by the technique of probability perturbation. The prior probability measure is perturbed so to give a positive prior probability to the null hypothesis, which would be null otherwise. This allows for the derivation of simple computational formulae for the Bayes factors. Numerical results reveal that, whenever the simulation scheme of the samples supports the null hypothesis, the null posterior probabilities appear systematically larger than their prior counterpart.

Suggested Citation

  • Sara Salvador & Riccardo Gatto, 2022. "Bayesian tests of symmetry for the generalized Von Mises distribution," Computational Statistics, Springer, vol. 37(2), pages 947-974, April.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01147-7
    DOI: 10.1007/s00180-021-01147-7
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    References listed on IDEAS

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    1. Toshihiro Abe & Arthur Pewsey & Kunio Shimizu, 2013. "Extending circular distributions through transformation of argument," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 833-858, October.
    2. Lidong Zhang & Qikai Li & Yuanjun Guo & Zhile Yang & Lei Zhang, 2018. "An Investigation of Wind Direction and Speed in a Featured Wind Farm Using Joint Probability Distribution Methods," Sustainability, MDPI, vol. 10(12), pages 1-15, November.
    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. 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.
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