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Negative Binomial Distribution

  1. Annibale Biggeri

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a10039

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Biggeri, A. 2005. Negative Binomial Distribution. Encyclopedia of Biostatistics. 5.

Author Information

  1. University of Florence, Florence, Italy

Publication History

  1. Published Online: 15 JUL 2005


The negative binomial distribution is an alternative to the Poisson distribution for modeling counts. It is useful when counts show more variation than the Poisson allows (overdispersion). This article shows two ways of deriving it, one way as a waiting time distribution for a certain number of successes with binary data, and the other way as a gamma mixture of Poisson distributions. It then discusses ways of estimating parameters, the use of the negative binomial distribution in regression models, and tests for overdispersion.


  • count data;
  • gamma distribution;
  • geometric distribution;
  • overdispersion;
  • Poisson distribution;
  • random effects;
  • waiting times