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A characterization of the exponential distribution involving absolute differences of i.i.d. random variables


Author: W. Stadje
Journal: Proc. Amer. Math. Soc. 121 (1994), 237-243
MSC: Primary 62E10
MathSciNet review: 1200180
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Abstract: A probability measure $ \mu $ on $ [0,\infty )$ is said to have property H if for independent random variables $ {X_1}$ and $ {X_2}$ distributed according to $ \mu $ the absolute difference $ \vert{X_1} - {X_2}\vert$ has the same distribution. Continuing previous work of Puri and Rubin we characterize the set of all distributions having property H.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1200180-1
Article copyright: © Copyright 1994 American Mathematical Society