Some properties of mutivariate distributions with pdf's constant on ellipsoids

Abstract

For random variables X₁...., X_K+1 with unbounded support, having a joint pdf constant on ellipsoids, the joint distribution of the ratios Y_i = X_i / X_k+1(1 ≤ i ≤ k) is obtained. If the X_i's have a spherically symmetric pdf. the Y_i's have a multivariate Cauchy distribution. The condition of unbounded support of the X_i's is not necessary, although it cannot always be relaxed.

Keywords:

• joint cntinuous distribution constant on ellipsoids
• spherically symmettric distribution
• multivariate cauchy distributions
• Fieller's distributions