Published online by Cambridge University Press: 14 July 2016
For independent random variables X and Y, if the conditional distribution of X given X + Y satisfies certain conditions, then the joint distribution of X and Y is a member of a certain one-parameter exponential family. Extensions for n independent random variables are given. A characterization for independent random variables involving order statistics is also given.
Research supported by Grant MCS 75–23344 from the U.S. National Science Foundation.