e/McCullagh's parametrization of the Cauchy distributions

Information
has gloss	eng: McCullagh's parametrization, introduced by Peter McCullagh, professor of statistics at the University of Chicago uses the two parameters of the non-standardised distribution to form a single complex-valued parameter, specifically, the complex number θ = μ + iσ, where i is the imaginary unit. It also extends the usual range of scale parameter to include σ < 0.
lexicalization	eng: McCullagh's parametrization of the Cauchy distributions
instance of	c/Continuous distributions