Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 1, 10-27

ON A TWO-PARAMETER FAMILY OF MULTIVARIATE UNIMODAL PROBABILITY MEASURES

By

EMILE BERTIN, Universiteit Utrecht, Utrecht

And

RADU THEODORESCU, Universit¢ e Laval, Qu¢ ebec

SUMMARY. The family of all random vectors X which are distributed as U Z, where the random variable U is .beta distributed and the random vector Z is independent of U, is examined within a general framework Bertain and Theodorescu( 1984) containing, e.g., versions of the theorem of Khinchin (1983) and the theorem of L¢ evy-Shepp (1962). This family leads to a new type of multivariate unimodality, providing a natural unifying background for several existing notions of unimodality.

 

AMS (1991) subject classification. 60E05, 60E10, 60E15.

Key words and phrases. Unimodality, generalized unimodality, theorem of Khinchin, theorem of Levy-shepp.

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