###
A NOTE ON CHARACTERIZATIONS OF

MULTIVARIATE STABLE DISTRIBUTIONS

###
TRUC T. NGUYEN^{1} AND ALLAN R. SAMPSON^{2}

^{1} *Department of Mathematics and Statistics, Bowling Green State University,*

Bowling Green, OH 43403, U.S.A.

^{2} *Department of Mathematics and Statistics, University of Pittsburgh,*

Pittsburgh, PA 15260, U.S.A.
(Received December 5, 1989; revised May 23, 1990)

**Abstract.**
Several characterizations of multivariate
stable distributions together with a characterization of
multivariate normal distributions and multivariate stable
distributions with Cauchy marginals are given. These are related
to some standard characterizations of Marcinkiewicz.

*Key words and phrases*:
Multivariate stable
distributions, Cauchy distribution, normal distribution,
Marcinkiewicz theorem.

**Source**
( TeX ,
DVI ,
PS )