On a Rao-Shanbhag characterization of the exponential/geometric distribution. (English) Zbl 1192.62033

Ferguson, Thomas S.

Sankhyā, Ser. A 64, No. 2, 246-255 (2002).

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 \(\{\min\{X,Y\} \leq u\}\) for some suitable values of \(u\), is discussed and a generalization to many variables is explored.

MSC:

62E10

Characterization and structure theory of statistical distributions

Keywords:

characterization by independence