  The (general) hypoexponential distribution is the distribution of a sum of
independent exponential random variables. We consider the particular case when
the involved exponential variables have distinct rate parameters. We prove that
the following converse result is true. If for some $n\ge 2$, $X_1,
X_2,\,\ldots,\,X_n$ are independent copies of a random variable $X$ with
unknown distribution $F$ and a specific linear combination of $X_j$'s has
hypoexponential distribution, then $F$ is exponential. Thus, we obtain new
characterizations of the exponential distribution. As corollaries of the main
results, we extend some previous characterizations established recently by
Arnold and Villase\~{n}or (2013) for a particular convolution of two random
variables.
