A note on characterizations based on truncated expectations

Many characterization results of the bivariate exponential distribution and the bivariate geometric distribution have been proved in the literature. Recently Nair and Nair (1988b, Ann. Inst. Statist. Math. 40 (2), 267-271) obtained a characterization result of the Gumbel bivariate exponential distribution and a bivariate geometric distribution based on truncated moments. In this note, we extend the results of Nair and Nair (1988b) to obtain a general result, characterizing these two bivariate distributions based on the truncated expectation of a function h, satisfying some mild conditions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.