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A Note on Inverse Stereographic Projection of Elliptical Distributions

Author

Listed:
  • Jean-Luc Dortet-Bernadet

    (Université de Strasbourg)

  • Nicolas Wicker

    (Université de Lille 1)

Abstract

This note concerns a family of distributions on the unit sphere obtained by inverse stereographic projection of elliptical distributions. We give some properties of these distributions with emphasis on the study of unimodality. This construction encompasses many known families of distributions on the unit sphere. Finally we show that it is possible to define new families of unimodal distributions that allow anisotropy.

Suggested Citation

  • Jean-Luc Dortet-Bernadet & Nicolas Wicker, 2018. "A Note on Inverse Stereographic Projection of Elliptical Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 138-151, February.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-017-0101-y
    DOI: 10.1007/s13171-017-0101-y
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    References listed on IDEAS

    as
    1. A. Kume & Andrew T. A. Wood, 2005. "Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants," Biometrika, Biometrika Trust, vol. 92(2), pages 465-476, June.
    2. 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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