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Explicit formulae for projectively transformed Cauchy distributions with applications

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  • Mendonça, Paulo R.S.
  • Lundell, Ben

Abstract

Cauchy distributions are characterized as the unique class of continuous distributions invariant to projective transformations, and this result naturally extends to the vector- and matrix-valued cases. We introduce a parameterization of Cauchy distributions that leads to elementary formulae for the parameters of projectively transformed matrix-valued Cauchy random variables, and illustrate an application of this result to the classical computer-vision problem of triangulation.

Suggested Citation

  • Mendonça, Paulo R.S. & Lundell, Ben, 2025. "Explicit formulae for projectively transformed Cauchy distributions with applications," Statistics & Probability Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000380
    DOI: 10.1016/j.spl.2025.110393
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    References listed on IDEAS

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    1. Phillips, P. C. B., 1989. "Spherical matrix distributions and cauchy quotients," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 51-53, May.
    2. Peter C.B. Phillips, 1989. "A New Proof of Knight's Theorem on the Cauchy Distribution," Cowles Foundation Discussion Papers 887, Cowles Foundation for Research in Economics, Yale University.
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