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Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients

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  • Zaigraev, Alexander
  • Kaniovski, Serguei

Abstract

We compute the minimum and maximum of the probability of k or more successes in n exchangeable Bernoulli trials as a function of the correlation coefficients. This probability finds wide application in reliability and decision theory. Since the probability is linear in the coefficients, finding the minimum and maximum requires solving linear programming problems. We show that the maximum can be lower than certainty (no certain success), whereas the minimum can be higher than zero (positive residual risk).

Suggested Citation

  • Zaigraev, Alexander & Kaniovski, Serguei, 2010. "Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1079-1084, July.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:13-14:p:1079-1084
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    References listed on IDEAS

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    1. Catalina Stefanescu & Bruce W. Turnbull, 2003. "Likelihood Inference for Exchangeable Binary Data with Varying Cluster Sizes," Biometrics, The International Biometric Society, vol. 59(1), pages 18-24, March.
    2. Y-C Hsieh, 2003. "New reliability bounds for coherent systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 995-1001, September.
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    Cited by:

    1. Pudney, Stephen & Diaz, Yadira, 2013. "Measuring poverty persistence with missing data with an application to Peruvian panel data," ISER Working Paper Series 2013-22, Institute for Social and Economic Research.
    2. Serkan Eryilmaz, 2017. "The concept of weak exchangeability and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 259-271, April.
    3. Di Cecco, Davide, 2011. "A geometric approach to a class of optimization problems concerning exchangeable binary variables," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 411-416, March.

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