IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v57y2002i4p363-373.html
   My bibliography  Save this article

Sums of dependent Bernoulli random variables and disease clustering

Author

Listed:
  • Yu, Chang
  • Zelterman, Daniel

Abstract

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00091-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chang Yu & Daniel Zelterman, 2002. "Statistical Inference for Familial Disease Clusters," Biometrics, The International Biometric Society, vol. 58(3), pages 481-491, September.
    2. Patricia M. E. Altham, 1978. "Two Generalizations of the Binomial Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(2), pages 162-167, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Minkova, Leda D. & Omey, Edward, 2011. "A new Markov Binomial distribution," Working Papers 2011/24, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    5. 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.
    6. Fama, Yuchen & Pozdnyakov, Vladimir, 2011. "A test for self-exciting clustering mechanism," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1541-1546, October.
    7. Chang Yu & Daniel Zelterman, 2002. "Statistical Inference for Familial Disease Clusters," Biometrics, The International Biometric Society, vol. 58(3), pages 481-491, September.
    8. 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.
    9. 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, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. repec:jss:jstsof:23:i08 is not listed on IDEAS
    3. 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.
    4. Bowman, Dale, 2016. "Statistical inference for familial disease models assuming exchangeability," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 220-225.
    5. 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.
    6. 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.
    7. Zhen Pang & Anthony Y. C. Kuk, 2007. "Test of Marginal Compatibility and Smoothing Methods for Exchangeable Binary Data with Unequal Cluster Sizes," Biometrics, The International Biometric Society, vol. 63(1), pages 218-227, March.
    8. C. D. Lai & K. Govindaraju & M. Xie, 1998. "Effects of correlation on fraction non-conforming statistical process control procedures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(4), pages 535-543.
    9. Timothy I. Cannings & Richard J. Samworth, 2017. "Random-projection ensemble classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 959-1035, September.
    10. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    11. Pires, Rubiane M. & Diniz, Carlos A.R., 2012. "Correlated binomial regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2513-2525.
    12. Molenberghs, Geert & Declerck, Lieven & Aerts, Marc, 1998. "Misspecifying the likelihood for clustered binary data," Computational Statistics & Data Analysis, Elsevier, vol. 26(3), pages 327-349, January.
    13. Iain L. MacDonald, 2021. "Is EM really necessary here? Examples where it seems simpler not to use EM," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 629-647, December.
    14. Sueli Mingoti, 2003. "A note on the sample size required in sequential tests for the generalized binomial distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(8), pages 873-879.
    15. Ardo Hout & Graciela Muniz-Terrera, 2019. "Hidden three-state survival model for bivariate longitudinal count data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 529-545, July.
    16. Dale Bowman & E. Olusegun George, 2017. "Weighted least squares estimation for exchangeable binary data," Computational Statistics, Springer, vol. 32(4), pages 1747-1765, December.
    17. Maria A. Spassova, 2019. "Statistical Approach to Identify Threshold and Point of Departure in Dose–Response Data," Risk Analysis, John Wiley & Sons, vol. 39(4), pages 940-956, April.
    18. Dittrich, R. & Hatzinger, R. & Katzenbeisser, W., 2002. "Modelling dependencies in paired comparison data: A log-linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 39-57, July.
    19. Dankmar Böhning, 2015. "Power series mixtures and the ratio plot with applications to zero-truncated count distribution modelling," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 201-216, August.
    20. Lovison, G., 1998. "An alternative representation of Altham's multiplicative-binomial distribution," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 415-420, January.
    21. Zhen Pang & Anthony Y. C. Kuk, 2005. "A Shared Response Model for Clustered Binary Data in Developmental Toxicity Studies," Biometrics, The International Biometric Society, vol. 61(4), pages 1076-1084, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:57:y:2002:i:4:p:363-373. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.