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An Over and Underdispersed Biparametric Extension of the Waring Distribution

Author

Listed:
  • Valentina Cueva-López

    (Department of Statistics and Operations Research, University of Jaén, 23071 Jaén, Spain
    These authors contributed equally to this work.)

  • María José Olmo-Jiménez

    (Department of Statistics and Operations Research, University of Jaén, 23071 Jaén, Spain
    These authors contributed equally to this work.)

  • José Rodríguez-Avi

    (Department of Statistics and Operations Research, University of Jaén, 23071 Jaén, Spain
    These authors contributed equally to this work.)

Abstract

A new discrete distribution for count data called extended biparametric Waring ( E B W ) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring ( U G W ) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the U G W distribution, the E B W can model both overdispersed and underdispersed data sets. In fact, the E B W distribution is a particular case of a U W G distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson ( C T P ) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the U G W model. We compare the E B W with the U G W by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.

Suggested Citation

  • Valentina Cueva-López & María José Olmo-Jiménez & José Rodríguez-Avi, 2021. "An Over and Underdispersed Biparametric Extension of the Waring Distribution," Mathematics, MDPI, vol. 9(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:170-:d:480886
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    References listed on IDEAS

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    1. Isola Ajiferuke, 1991. "A probabilistic model for the distribution of authorships," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 42(4), pages 279-289, May.
    2. Panaretos, John & Xekalaki, Evdokia, 1986. "The stuttering generalized waring distribution," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 313-318, October.
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