Exponential and Hypoexponential Distributions: Some Characterizations

George P. Yanev
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George P. Yanev: Center for Vector-Borne Diseases, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA

Mathematics, 2020, vol. 8, issue 12, 1-10

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 , 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.

Keywords: exponential distribution; hypoexponential distribution; characterizations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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