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A new bivariate negative binomial distribution

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  • C. R. Mitchell
  • A. S. Paulson

Abstract

A new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.

Suggested Citation

  • C. R. Mitchell & A. S. Paulson, 1981. "A new bivariate negative binomial distribution," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(3), pages 359-374, September.
    • Handle: RePEc:wly:navlog:v:28:y:1981:i:3:p:359-374
    DOI: 10.1002/nav.3800280302
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    Cited by:

    1. Mathews Joseph & Bhattacharya Sumangal & Das Ishapathik & Sen Sumen, 2022. "Multiple inflated negative binomial regression for correlated multivariate count data," Dependence Modeling, De Gruyter, vol. 10(1), pages 290-307, January.
    2. Alessandro Barbiero, 2022. "Discrete analogues of continuous bivariate probability distributions," Annals of Operations Research, Springer, vol. 312(1), pages 23-43, May.
    3. Alessandro Barbiero, 2022. "Properties and estimation of a bivariate geometric model with locally constant failure rates," Annals of Operations Research, Springer, vol. 312(1), pages 3-22, May.
    4. Barbiero, A., 2019. "A bivariate count model with discrete Weibull margins," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 91-109.

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