CHARACTERISATIONS OF THE GEOMETRIC DISTRIBUTION USING
DISTRIBUTIONAL PROPERTIES OF THE ORDER STATISTICS
Abstract: Let
be independent, identically distributed, non-negative integer
valued random variables and let

denote the corresponding order statistics. If

for all

and

then the distribution of

is geometric. We modify this distributional property
of the order statistics in several directions to obtain characterisations of the geometric
distribution. We provide examples to show that the assumptions, in some respect, cannot be
weakened any further.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -