On a Rao-Shanbhag Characterization
of the Exponential/Geometric Distribution
Thomas S. FERGUSON
University of California at Los Angeles
Abstract:
A theorem of Rao and Shanbhag, characterizing the
exponential and the geometric distributions as the only distributions
of independent random variables, X and Y, for which X-Y is independent
of the event min{X,Y}<u for some suitable values of u, is
discussed and a generalization to many variables is explored.