A Simple Method for Generating Correlated Binary Variates

Chul Gyu Park, Taesung Park, Dong Wan Shin

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108 Scopus citations


Correlated binary data are frequently analyzed in studies of repeated measurements, reliability analysis, and others. In such studies correlations among binary variables are usually nonnegative. This article provides a simple algorithm for generating an arbitrary dimensional random vector of non-negatively correlated binary variables. In some frequently encountered situations the algorithm reduces to explicit expressions. The correlated binary variables are generated from correlated Poisson variables. The key idea lies in the property that any Poisson random variable can be expressed as a convolution of other independent Poisson random variables. The binary variables have desired correlations by sharing common independent Poisson variables.

Original languageEnglish
Pages (from-to)306-310
Number of pages5
JournalAmerican Statistician
Issue number4
StatePublished - Nov 1996

Bibliographical note

Funding Information:
Chul Gyu Park is Assistant Professor, Department of Applied Statistics, University of Suwon, 445-743, Suwon, South Korea. Taesung Park is Associate Professor, Department of Statistics, Hankuk University of Foreign Studies, Seoul, 449-791, South Korea, and the National Institute of Child Health and Human Development, Bethesda, MD 20892. Dong Wan Shin is Associate Professor, Department of Statistics, Ewha Womans University, Seoul, 120-750, South Korea. The authors thank an associate editor, two referees, and Professors Beong So0 So and You Sung Park for valuable suggestions and comments. This work was supported by Directed Research grant 94-0701-01-01-3 from the Korea Science and Engineering Foundation.


  • Generalized estimating equations
  • Poisson variables
  • Random number generation


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