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Testing for the bivariate Poisson distribution

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  • F. Novoa-Muñoz
  • M. Jiménez-Gamero

Abstract

This paper studies goodness-of-fit tests for the bivariate Poisson distribution. Specifically, we propose and study several Cramér–von Mises type tests based on the empirical probability generating function. They are consistent against fixed alternatives for adequate choices of the weight function involved in their definition. They are also able to detect local alternatives converging to the null at a certain rate. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approximation and compares their powers for finite sample sizes. Extensions for testing goodness-of-fit for the multivariate Poisson distribution are also discussed. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:6:p:771-793
    DOI: 10.1007/s00184-013-0464-6
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    References listed on IDEAS

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    1. Karlis, Dimitris & Ntzoufras, Ioannis, 2005. "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i10).
    2. Meintanis, Simos & Swanepoel, Jan, 2007. "Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1004-1013, June.
    3. Baringhaus, L. & Henze, N., 1992. "A goodness of fit test for the Poisson distribution based on the empirical generating function," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 269-274, March.
    4. 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.
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