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On the three-dimensional negative binomial distribution

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  • Camilla Mondrup Andreassen
  • Jens Ledet Jensen

Abstract

We consider a particular generalization of the negative binomial distribution to the multivariate case obtained through a specification of the probability generating function as the negative power of a certain polynomial. The probability function itself has previously been derived for the two-dimensional case only, and inference in the multivariate negative binomial distribution has been restricted to the use of composite likelihood based on one- or two-dimensional marginals. In this article, we derive the three-dimensional probability function as a sum with all terms positive and study the range of possible parameter values. We illustrate the use of the three-dimensional distribution for modeling three correlated SAR images.

Suggested Citation

  • Camilla Mondrup Andreassen & Jens Ledet Jensen, 2018. "On the three-dimensional negative binomial distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(10), pages 2314-2326, May.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:10:p:2314-2326
    DOI: 10.1080/03610926.2013.864766
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