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.

Read more about this topic:  Cauchy Distribution

Famous quotes containing the word properties:

    “The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
    —John Locke (1632–1704)