On a characterization of exponential and double exponential distributions

03/20/2022

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by   Reza Rastegar, et al.

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Recently, G. Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev's theorem by relaxing a restriction on the sign of mixture coefficients and, in addition, obtain a similar characterization for the Laplace family of distributions.