Multivariate Doubly-Inflated Negative Binomial Distribution Using Gaussian Copula

  • Joseph Mathews
  • Sumen SenEmail author
  • Ishapathik Das
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)


Studies involving count data appear frequently in the social and natural sciences. Moreover, this data often has a non-normal structure making it difficult to model. Many of these models have inflation points centered around zero and potentially at an additional inflation point. We present a model for doubly-inflated count data using the negative binomial distribution. To maintain the correlation structure, we also use Gaussian copula methods. We provide visuals of the bivariate negative binomial Gaussian copula as well as the bivariate doubly-Inflated negative binomial model. Additionally, we give the expression for the proposed model’s marginal distribution and the nth order moments. Finally, we present an algorithm for estimating the doubly-inflated negative binomial model’s parameters. A table of the results is given with mean square error (MSE) values for each parameter obtained.


Inflated negative binomial Copula Gaussian copula 


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAustin Peay State UniversityClarksvilleUSA
  2. 2.Department of MathematicsIndian Institute of Technology TirupatiTirupatiIndia

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