#### Document Type

Article

#### Publication Date

12-12-2020

#### Abstract

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 ≥ 2, X1, X2, . . . , Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj ’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 Villaseñor (2013) for a particular convolution of two random variables.

#### Recommended Citation

Yanev, G.P. Exponential and Hypoexponential Distributions: Some Characterizations. Mathematics 2020, 8, 2207.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

#### DOI

10.3390/math8122207