UNIFORM MIXTURES VIA POSTERIOR MEANS

ARJUN K. GUPTA^{1} AND JACEK WESOLOWSKI^{2}

1Department of Mathematics and Statistics, Bowling Green State University,

Bowling Green, OH 43403-0221, U.S.A. 2Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

(Received June 5, 1995; revised February 19, 1996)

Abstract. The problem of identification of uniform mixtures via posterior means is studied. For linear posterior means a complete solution is given. It determines a family of prior distributions involving beta of both kinds and gamma. Identifiability via any consistent posterior mean is also investigated.

Key words and phrases: Mixtures, posterior mean, identification, characterization of probability distribution, uniform conditional distribution, conditional moments, linearity of regression, gamma distribution, beta type distributions.