A NOTE ON CHARACTERIZATIONS OF MULTIVARIATE STABLE DISTRIBUTIONS

A NOTE ON CHARACTERIZATIONS OF
MULTIVARIATE STABLE DISTRIBUTIONS

TRUC T. NGUYEN¹ AND ALLAN R. SAMPSON²

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.

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