Sankhya: The Indian Journal of Statistics1997, Volume 59, Series A, Pt. 1, 10-27
ON A TWO-PARAMETER FAMILY OF MULTIVARIATE UNIMODAL PROBABILITY MEASURES
EMILE BERTIN, Universiteit Utrecht, Utrecht
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.
Full paper (PDF)
This article in Mathematical Reviews