Log-concavity of probability of occurrence of at least r independent events

Y. S. Sathe and S. M. Bendre

Statistics & Probability Letters, 1991, vol. 11, issue 1, 63-64

Abstract: For a sequence of n independent events, it is shown that the sequences of the probability of occurrence of at least r events and the probability of occurrence of at most r - 1 events are both log-concave. The log-concavity of the sequence of distribution functions of order statistics follows as a corollary. Further, a counter example is given to show that the result does not hold for dependent events.

Keywords: Log-concavity; independent; events; order; statistics (search for similar items in EconPapers)
Date: 1991
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