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A bivariate Poisson count data model using conditional probabilities

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  • Peter Berkhout
  • Erik Plug

Abstract

The applied econometrics of bivariate count data predominantly focus on a bivariate Poisson density with a correlation structure that is very restrictive. The main limitation is that this bivariate distribution excludes zero and negative correlation. This paper introduces a new model which allows for a more flexible correlation structure. To this end the joint density is decomposed by means of the multiplication rule in marginal and conditional densities. Simulation experiments and an application of the model to recreational data are presented.

Suggested Citation

  • Peter Berkhout & Erik Plug, 2004. "A bivariate Poisson count data model using conditional probabilities," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 349-364, August.
  • Handle: RePEc:bla:stanee:v:58:y:2004:i:3:p:349-364
    DOI: 10.1111/j.1467-9574.2004.00126.x
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    File URL: https://doi.org/10.1111/j.1467-9574.2004.00126.x
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    Cited by:

    1. Lundevaller, Erling Häggström, 2009. "The effect of travel cost on frequencies of shopping and recreational trips in Sweden," Journal of Transport Geography, Elsevier, vol. 17(3), pages 208-215.
    2. Xiaoping Jin & Bradley P. Carlin & Sudipto Banerjee, 2005. "Generalized Hierarchical Multivariate CAR Models for Areal Data," Biometrics, The International Biometric Society, vol. 61(4), pages 950-961, December.
    3. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    4. F. Novoa-Muñoz & M. Jiménez-Gamero, 2014. "Testing for the bivariate Poisson distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 771-793, August.
    5. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    6. Rajib Dey & M. Ataharul Islam, 2017. "A conditional count model for repeated count data and its application to GEE approach," Statistical Papers, Springer, vol. 58(2), pages 485-504, June.
    7. Jacek Osiewalski & Jerzy Marzec, 2019. "Joint modelling of two count variables when one of them can be degenerate," Computational Statistics, Springer, vol. 34(1), pages 153-171, March.
    8. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    9. Tsung-Shan Tsou, 2016. "Robust likelihood inference for multivariate correlated count data," Computational Statistics, Springer, vol. 31(3), pages 845-857, September.

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