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

1 January 1975

journal article
research article
Published by Taylor & Francis in Communications in Statistics

Vol. 4 (12) , 1157-1160
https://doi.org/10.1080/03610927508827323

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

This publication has 1 reference indexed in Scilit:

THE DISTRIBUTION OF THE INDEX IN A NORMAL BIVARIATE POPULATION
Biometrika, 1932