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

Stadje, W.

doi:10.1090/S0002-9939-1994-1200180-1

A characterization of the exponential distribution involving absolute differences of i.i.d. random variables
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by W. Stadje PDF

Proc. Amer. Math. Soc. 121 (1994), 237-243 Request permission

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 $|{X_1} - {X_2}|$ 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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