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Sums of dependent Bernoulli random variables and disease clustering


  • Yu, Chang
  • Zelterman, Daniel


We develop new discrete distributions that describe the behavior of a sum of dependent Bernoulli random variables. These distributions are motivated by the manner in which multiple individuals with a lung disease appear to cluster within the same family. General results for these models include recursive relationships for their mass functions and moments.

Suggested Citation

  • Yu, Chang & Zelterman, Daniel, 2002. "Sums of dependent Bernoulli random variables and disease clustering," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 363-373, May.
  • Handle: RePEc:eee:stapro:v:57:y:2002:i:4:p:363-373

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    Cited by:

    1. Fama, Yuchen & Pozdnyakov, Vladimir, 2011. "A test for self-exciting clustering mechanism," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1541-1546, October.
    2. Gianfranco Lovison, 2015. "A generalization of the Binomial distribution based on the dependence ratio," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 126-149, May.
    3. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.
    4. Rodrigues, Josemar & Bazán, Jorge L. & Suzuki, Adriano K. & Balakrishnan, Narayanaswamy, 2016. "The Bayesian restricted Conway–Maxwell-Binomial model to control dispersion in count data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 281-288.
    5. Ramesh Gupta & Hui Tao, 2010. "A generalized correlated binomial distribution with application in multiple testing problems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 59-77, January.
    6. Minkova, Leda D. & Omey, Edward, 2011. "A new Markov Binomial distribution," Working Papers 2011/24, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    7. I. Ricard & A. C. Davison, 2007. "Statistical inference for olfactometer data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 479-492.
    8. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy & Bazán, Jorge, 2014. "A COM–Poisson type generalization of the binomial distribution and its properties and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 158-166.


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