Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 2, 246--255

ON A RAO-SHANBHAG CHARACTERIZATION OF THE EXPONENTIAL/GEOMETRIC DISTRIBUTION

By

THOMAS S. FERGUSON University of California, Los Angeles, USA

SUMMARY. A theorem of Rao and Shanbhag, characterizing the exponential and the geometric distributions as the only distributions of independent $X$ and $Y$ for which $X-Y$ is independent of $\{\min\{X,Y\} \le u\}$ for some suitable values of $u$, is discussed and a generalization to many variables is explored.

*AMS (1991) subject classification}. *62E05, 62H05.

*Key words and phrases. *Characterization by independence, Lau-Rao Theorem.