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New inference procedures for generalized Poisson distributions

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  • Simos Meintanis

Abstract

A common feature for compound Poisson and Katz distributions is that both families may be viewed as generalizations of the Poisson law. In this paper, we present a unified approach in testing the fit to any distribution belonging to either of these families. The test involves the probability generating function, and it is shown to be consistent under general alternatives. The asymptotic null distribution of the test statistic is obtained, and an effective bootstrap procedure is employed in order to investigate the performance of the proposed test with real and simulated data. Comparisons with classical methods based on the empirical distribution function are also included.

Suggested Citation

  • Simos Meintanis, 2008. "New inference procedures for generalized Poisson distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 751-762.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:7:p:751-762
    DOI: 10.1080/02664760801997174
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    References listed on IDEAS

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    1. Bosch, Ronald J. & Ryan, Louise M., 1998. "Generalized poisson models arising from Markov processes," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 205-212, August.
    2. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2005. "Bootstrapping modified goodness-of-fit statistics with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 111-121, February.
    3. Wang, Y. H. & Ji, Shuixin, 1993. "Derivations of the compound Poisson distribution and process," Statistics & Probability Letters, Elsevier, vol. 18(1), pages 1-7, August.
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    Cited by:

    1. Simos Meintanis & Dimitris Karlis, 2014. "Validation tests for the innovation distribution in INAR time series models," Computational Statistics, Springer, vol. 29(5), pages 1221-1241, October.
    2. Apostolos Batsidis & María Dolores Jiménez-Gamero & Artur J. Lemonte, 2020. "On goodness-of-fit tests for the Bell distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 297-319, April.
    3. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2019. "Testing for the Poisson–Tweedie distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 146-162.

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