Resumo

MAZUCHELI, Josmar; BERTOLI, Wesley  e  OLIVEIRA, Ricardo. Two Useful Discrete Distributions to Model Overdispersed Count Data. Rev.Colomb.Estad. [online]. 2020, vol.43, n.1, pp.21-48.  Epub 05-Jun-2020. ISSN 0120-1751.  https://doi.org/10.15446/rce.v43n1.77052.

The methods to obtain discrete analogs of continuous distributions have been widely considered in recent years. In general, the discretization process provides probability mass functions that can be competitive with the tra ditional model used in the analysis of count data, the Poisson distribution. The discretization procedure also avoids the use of continuous distribution in the analysis of strictly discrete data. In this paper, we seek to introduce two discrete analogs for the Shanker distribution using the method of the in finite series and the method based on the survival function as alternatives to model overdispersed datasets. Despite the difference between discretization methods, the resulting distributions are interchangeable. However, the dis tribution generated by the method of the infinite series method has simpler mathematical expressions for the shape, the generating functions, and the central moments. The maximum likelihood theory is considered for estima tion and asymptotic inference concerns. A simulation study is carried out in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed models is evaluated using real datasets pro vided by the literature.

Palavras-chave : Maximum likelihood estimation; Discrete distributions; Monte Carlo simulation; Overdispersion; Shanker distribution.

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