Cauchy Distribution - Transformation Properties

Transformation Properties

  • If then
  • If then
  • If and are independent, then
  • If then
  • McCullagh's parametrization of the Cauchy distributions: Expressing a Cauchy distribution in terms of one complex parameter, define X ~ Cauchy to mean X ~ Cauchy. If X ~ Cauchy then:
~ Cauchy where a,b,c and d are real numbers.
  • Using the same convention as above, if X ~ Cauchy then:
~ CCauchy
where "CCauchy" is the circular Cauchy distribution.

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