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A family of consistent normally distributed tests for Poissonity

Author

Listed:
  • Antonio Di Noia

    (University of Siena)

  • Marzia Marcheselli

    (University of Siena
    NBFC, National Biodiversity Future Center)

  • Caterina Pisani

    (University of Siena
    NBFC, National Biodiversity Future Center)

  • Luca Pratelli

    (Naval Academy)

Abstract

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted alternatives to the Poisson distribution. Actually, the family of test statistics is based on the difference between the plug-in estimator of the Poisson cumulative distribution function and the empirical cumulative distribution function. The test statistics have an intuitive and simple form and are asymptotically normally distributed, allowing a straightforward implementation of the test. The finite sample properties of the test are investigated by means of an extensive simulation study. The test shows satisfactory behaviour compared to other tests with known limit distribution.

Suggested Citation

  • Antonio Di Noia & Marzia Marcheselli & Caterina Pisani & Luca Pratelli, 2024. "A family of consistent normally distributed tests for Poissonity," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(1), pages 209-223, March.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:1:d:10.1007_s10182-023-00478-8
    DOI: 10.1007/s10182-023-00478-8
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    References listed on IDEAS

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    1. Christian H. Weiß & Annika Homburg & Pedro Puig, 2019. "Testing for zero inflation and overdispersion in INAR(1) models," Statistical Papers, Springer, vol. 60(3), pages 823-848, June.
    2. 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.
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