On a Characterization of Exponential and Double Exponential Distributions
Accepted: January 2023
Keywords:hypoexponential distribution, Laplace distribution, characterization of distributions, sums of independent random variables, characteristic functions, functional equations
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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