On Zero-Modified Poisson-Sujatha Distribution to Model Overdispersed Count Data

  • Wesley Bertoli da Silva Federal Technology University of Paraná
  • Angélica Maria Tortola Ribeiro Federal Technology University of Paraná
  • Katiane Silva Conceição University of São Paulo
  • Marinho Gomes Andrade University of São Paulo
  • Francisco Louzada Neto University of São Paulo

Abstract

In this paper we propose the zero-modified Poisson-Sujatha distribution as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. It will be shown that the zero modification can be incorporated by using the zero-truncated Poisson-Sujatha distribution. A simple reparametrization of the probability function will allow us to represent the zero-modified Poisson-Sujatha distribution as a hurdle model. This trick leads to the fact that proposed model can be fitted without any previously information about the zero modification present in a given dataset. The maximum likelihood theory will be used for parameter estimation and asymptotic inference concerns. A simulation study will be conducted in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed model will be illustrated using real datasets of the biological sciences field and comparing it with other models available in the literature.

Author Biographies

Wesley Bertoli da Silva, Federal Technology University of Paraná

Department of Mathematics

Angélica Maria Tortola Ribeiro, Federal Technology University of Paraná

Department of Mathematics

Katiane Silva Conceição, University of São Paulo

Institute of Mathematics and Computer Sciences
Department of Statistics

Marinho Gomes Andrade, University of São Paulo
Institute of Mathematics and Computer Sciences
Department of Statistics
Francisco Louzada Neto, University of São Paulo
Institute of Mathematics and Computer Sciences
Department of Statistics

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Published
2018-05-27
How to Cite
da Silva, W. B., Ribeiro, A. M. T., Conceição, K. S., Andrade, M. G., & Neto, F. L. (2018). On Zero-Modified Poisson-Sujatha Distribution to Model Overdispersed Count Data. Austrian Journal of Statistics, 47(3), 1-19. https://doi.org/10.17713/ajs.v47i3.590