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Characterizations of the geometric distribution by distributional properties

Published online by Cambridge University Press:  14 July 2016

Mynt Zijlstra
Mynt Zijlstra*
Affiliation:
Nederlandse Philips Bedrijven BV
*
∗ Postal address: Nederlandse Philips Bedrijven BV, ISA-CQM, Building VN-706, P.O. Box 218, 5600 MD Eindhoven, The Netherlands.
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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.

Keywords

LACK OF MEMORYORDER STATISTICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 843 - 850
Copyright
Copyright © Applied Probability Trust 1983 

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