On characterization of the exponential distribution via hypoexponential distributions

TL;DR

This paper characterizes the exponential distribution by examining cases where the sum of independent exponential variables results in a hypoexponential distribution with all but one rate identical, extending previous characterizations.

Contribution

It provides a new characterization of the exponential distribution specifically for the case where all but one rate parameters are identical, complementing existing hypoexponential characterizations.

Findings

Proves a new characterization of exponential distribution in a specific hypoexponential case.

Extends previous hypoexponential characterizations to include cases with repeated rate parameters.

Connects the mathematical properties to molecular biology applications.

Abstract

The sum of independent, but not necessary identically distributed, exponential random variables follows 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.