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arXiv · 2203.10495

On a characterization of exponential and double exponential distributions

Reza Rastegar·Alex Roitershtein
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Abstract

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.

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Reza Rastegar, Alex Roitershtein. 2022-03-20. On a characterization of exponential and double exponential distributions. https://arxiv.org/abs/2203.10495

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