On characterization of the exponential distribution via hypoexponential distributions

04/02/2022

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by   George Yanev, et al.

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The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We study a situation when the rate parameters of the exponential variables are not all different from each other. We obtain a representation for the Laplace transform of the hypoexponential distribution in the case of two repeated parameter values. Applying this decomposition, we prove a characterization of the exponential distribution.