On a characterization of exponential and double exponential distributions

TL;DR

This paper extends a characterization of exponential distributions by relaxing previous restrictions and also provides a similar characterization for Laplace distributions, broadening understanding of these distribution families.

Contribution

It generalizes Yanev's theorem on exponential distributions and introduces a new characterization for Laplace distributions.

Findings

Extended Yanev's theorem with relaxed conditions

Provided a new characterization for Laplace distributions

Broadened the theoretical understanding of distribution characterizations

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.