Exponential and Hypoexponential Distributions: Some Characterizations

12/15/2020

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by   George P. Yanev, et al.

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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, X_1, X_2, …, 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 Villaseñor (2013) for a particular convolution of two random variables.