The sum of independent, but not necessary identically distributed, exponential random variables follows a hypoexponential distribution. We focus on a particular case when all but one rate parameters of the exponential variables are identical. This is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.
Yanev, G. On Characterization of the Exponential Distribution Via Hypoexponential Distributions. J Stat Theory Pract 17, 30 (2023). https://doi.org/10.1007/s42519-023-00327-6
Journal of Statistical Theory and Practice