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

Author

Listed:
  • Sathe, Y. S.
  • Bendre, S. M.

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.

Suggested Citation

  • Sathe, Y. S. & Bendre, S. M., 1991. "Log-concavity of probability of occurrence of at least r independent events," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 63-64, January.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:1:p:63-64
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