Characterizations of the geometric distribution by distributional properties

Abstract

Some new characterizations of the geometric distribution are studied. A generalization of the characterization by the well-known ‘lack-of-memory' property is given together with some closely related characterizations. Furthermore the modified geometric distribution is characterized by a distributional property of the difference of two successive order statistics. The latter result extends work of Puri and Rubin (1970). Finally the geometric distribution is characterized by a conditional distribution property of the difference of two arbitrary order statistics, which generalizes a result by Arnold (1980). Some of the results given answer open questions put in earlier papers.