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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 10, Fasc. 1,
pages 143 - 147
 

CHARACTERISATIONS OF THE GEOMETRIC DISTRIBUTION USING DISTRIBUTIONAL PROPERTIES OF THE ORDER STATISTICS

Sitadri Nath Bagchi

Abstract: Let X ,X ,...,X
 1   2     N  be independent, identically distributed, non-negative integer valued random variables and let

X    < X    < ...< X
  1:N    2:N         N:N
denote the corresponding order statistics. If P(X1:N > k) = P(X1 > N k) for all N > 1 and k = 1, then the distribution of X1  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: -

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