Explicit formulae for projectively transformed Cauchy distributions with applications

Paulo R.S. Mendonça and Ben Lundell

Statistics & Probability Letters, 2025, vol. 222, issue C

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.

Keywords: Matrix-valued Cauchy distribution; Projective transformation; Triangulation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110393

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