Abstract
In this note, a characterization of the Gumbel's bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhyā Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.
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Muraleedharan Nair, K.R., Unnikrishnan Nair, N. On characterizing the bivariate exponential and geometric distributions. Ann Inst Stat Math 40, 267–271 (1988). https://doi.org/10.1007/BF00052343
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DOI: https://doi.org/10.1007/BF00052343