Abstract
The purpose of the present paper is to prove that (1) the ratio of two independent stable random variables with exponent d and skewness 0 is equal in distribution to a standard Cauchy multiplied by $sin(pi d R / 2) / sin( pi d (1-R)/2 )^1/d$, where R is a Uniform0,1 random variabel; and (2) the same ratio except with skewness parameter beta is equal to $W_1(\beta) W_2(\beta) \sin(pi d R / 2) / \sin( pi d (1-R)/2 )^1/d$, where $W(0)$ is a standard Cauchy, and $W(\beta) = W(0) \cos(\beta/2) + \sin( \beta/2 )$.
Users
Please
log in to take part in the discussion (add own reviews or comments).