IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v164y2019icp146-162.html
   My bibliography  Save this article

Testing for the Poisson–Tweedie distribution

Author

Listed:
  • Jiménez-Gamero, M.D.
  • Alba-Fernández, M.V.

Abstract

In practice, count data exhibit over-dispersion, zero-inflation and even heavy tails. The Poisson–Tweedie distribution is a flexible parametric family able to accommodate these features. This paper proposes and studies a computationally convenient goodness-of-fit test for this distribution, which is based on an empirical counterpart of a system of equations. The test is consistent against fixed alternatives. The null distribution of the test can be consistently approximated by a parametric bootstrap. The goodness of the bootstrap estimator and the power for finite sample sizes are numerically assessed. Comparisons with other tests are also included. Applications to two real data sets are displayed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:164:y:2019:i:c:p:146-162
    DOI: 10.1016/j.matcom.2018.08.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418301988
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.08.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nakamura, Miguel & Perez-Abreu, Victor, 1993. "Empirical probability generating function : An overview," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 287-295, June.
    2. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    3. Simos Meintanis, 2008. "New inference procedures for generalized Poisson distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 751-762.
    4. M. D. Jiménez-Gamero & A. Batsidis, 2017. "Minimum distance estimators for count data based on the probability generating function with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 503-545, July.
    5. Zhu, Rong & Joe, Harry, 2009. "Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1695-1703, August.
    6. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    7. Cui, Yunwei & Zheng, Qi, 2017. "Conditional maximum likelihood estimation for a class of observation-driven time series models for count data," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 193-201.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2017. "Tests for Structural Changes in Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 843-865, December.
    3. M. D. Jiménez-Gamero & A. Batsidis, 2017. "Minimum distance estimators for count data based on the probability generating function with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 503-545, July.
    4. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2021. "A test for the geometric distribution based on linear regression of order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 103-123.
    5. Kim, Dukpa & Oka, Tatsushi & Estrada, Francisco & Perron, Pierre, 2020. "Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures," Journal of Econometrics, Elsevier, vol. 214(1), pages 130-152.
    6. Weiß, Christian H. & Steuer, Detlef & Jentsch, Carsten & Testik, Murat Caner, 2018. "Guaranteed conditional ARL performance in the presence of autocorrelation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 367-379.
    7. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    8. Lucio Barabesi & Carolina Becatti & Marzia Marcheselli, 2018. "The Tempered Discrete Linnik distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 45-68, March.
    9. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, vol. 3(2), pages 1-21, May.
    10. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2024. "Predictive ability tests with possibly overlapping models," Journal of Econometrics, Elsevier, vol. 241(1).
    11. Davidson, Russell & Trokić, Mirza, 2020. "The fast iterated bootstrap," Journal of Econometrics, Elsevier, vol. 218(2), pages 451-475.
    12. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    13. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    14. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    15. Christian H. Weiß & Esmeralda Gonçalves & Nazaré Mendes Lopes, 2017. "Testing the compounding structure of the CP-INARCH model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 571-603, July.
    16. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    17. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    18. González, Andrés & Teräsvirta, Timo & van Dijk, Dick & Yang, Yukai, 2005. "Panel Smooth Transition Regression Models," SSE/EFI Working Paper Series in Economics and Finance 604, Stockholm School of Economics, revised 11 Oct 2017.
    19. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    20. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:164:y:2019:i:c:p:146-162. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.