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On the Discrete Quasi Xgamma Distribution

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Abstract

Methods to obtain discrete analogs of continuous distributions have been widely applied in recent years. In general, the discretization process provides probability mass functions that can be competitive with traditional models used in the analysis of count data. The discretization procedure also avoids the use of continuous distribution to model strictly discrete data. In this paper, we propose two discrete analogs for the quasi xgamma distribution as alternatives to model under- and overdispersed datasets. The methods of infinite series and survival function have been considered to derive the models and, despite the difference between the methods, the resulting distributions are interchangeable. Several statistical properties of the proposed models have been derived. The maximum likelihood theory has been considered for estimation and asymptotic inference concerns. An intensive simulation study has been carried out in order to evaluate the main properties of the maximum likelihood estimators. The usefulness of the proposed models has been assessed by using two real datasets provided by literature. A general comparison of the proposed models with some well-known discrete distributions has been provided.

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Acknowledgements

Josmar Mazucheli gratefully acknowledge the partial financial support from Fundação Araucária (Grant 064/2019 - UEM/Fundação Araucá). The research of Wesley Bertoli is partially supported by the Federal University of Technology - Paraná and by a doctoral grant from Fundação Araucária (CP 18/2015). The Brazilian organization CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) supports the research of Ricardo P. Oliveira (GC 001).

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Authors and Affiliations

  1. Department of Statistics, State University of Maringá, Maringá, PR, 87020-900, Brazil

    Josmar Mazucheli & André F. B. Menezes

  2. Department of Statistics, Federal University of Technology - Paraná, Curitiba, PR, 80230-901, Brazil

    Wesley Bertoli

  3. Medical School of Ribeirão Preto, University of São Paulo, Ribeirão Preto, SP, 14049-900, Brazil

    Ricardo P. Oliveira

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  1. Josmar Mazucheli
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  2. Wesley Bertoli
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  3. Ricardo P. Oliveira
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  4. André F. B. Menezes
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Correspondence to Josmar Mazucheli.

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Mazucheli, J., Bertoli, W., Oliveira, R.P. et al. On the Discrete Quasi Xgamma Distribution. Methodol Comput Appl Probab 22, 747–775 (2020). https://doi.org/10.1007/s11009-019-09731-7

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  • DOI: https://doi.org/10.1007/s11009-019-09731-7

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