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

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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.

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