IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v77y2014i6p771-793.html
   My bibliography  Save this article

Testing for the bivariate Poisson distribution

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-013-0464-6
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00184-013-0464-6?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. 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.
    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. 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.
    2. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    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. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    5. 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.
    6. 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.
    7. 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.
    8. Vijay Viswanathan & Sebastian Tillmanns & Manfred Krafft & Daniel Asselmann, 2018. "Understanding the quality–quantity conundrum of customer referral programs: effects of contribution margin, extraversion, and opinion leadership," Journal of the Academy of Marketing Science, Springer, vol. 46(6), pages 1108-1132, November.
    9. Székely, Gábor J. & Rizzo, Maria L., 2004. "Mean distance test of Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 241-247, April.
    10. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    11. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.
    12. Baringhaus, Ludwig & Taherizadeh, Fatemeh, 2010. "Empirical Hankel transforms and its applications to goodness-of-fit tests," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1445-1457, July.
    13. 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.
    14. K. Chua & S. Ong, 2013. "Test of misspecification with application to negative binomial distribution," Computational Statistics, Springer, vol. 28(3), pages 993-1009, June.
    15. Rómulo A. Chumacero, 2009. "Altitude or Hot Air?," Journal of Sports Economics, , vol. 10(6), pages 619-638, December.
    16. Shanmugam R, 2018. "Impact of Raising Copayment and/or Reducing Reimbursement Benefits on Healthcare according to “Disequilibrium Bivariate Distributionâ€," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 5(1), pages 1-13, February.
    17. M Ataharul Islam & Rafiqul I Chowdhury, 2017. "A generalized right truncated bivariate Poisson regression model with applications to health data," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-13, June.
    18. Hofer, Vera & Leitner, Johannes, 2017. "Relative pricing of binary options in live soccer betting markets," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 66-85.
    19. Lluís Bermúdez & Dimitris Karlis, 2022. "Copula-based bivariate finite mixture regression models with an application for insurance claim count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1082-1099, December.
    20. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2015. "An approximation to the null distribution of a class of Cramér–von Mises statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 258-272.

    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:spr:metrik:v:77:y:2014:i:6:p:771-793. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.springer.com .

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.