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On the Discrete Quasi Xgamma Distribution

Author

Listed:
  • Josmar Mazucheli

    (State University of Maringá)

  • Wesley Bertoli

    (Federal University of Technology - Paraná)

  • Ricardo P. Oliveira

    (University of São Paulo)

  • André F. B. Menezes

    (State University of Maringá)

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.

Suggested Citation

  • Josmar Mazucheli & Wesley Bertoli & Ricardo P. Oliveira & André F. B. Menezes, 2020. "On the Discrete Quasi Xgamma Distribution," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 747-775, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09731-7
    DOI: 10.1007/s11009-019-09731-7
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    References listed on IDEAS

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    1. J. H. C. Lisman & M. C. A. van Zuylen, 1972. "Note on the generation of most probable frequency distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 26(1), pages 19-23, March.
    2. Subrata Chakraborty & Rameshwar D. Gupta, 2015. "Exponentiated Geometric Distribution: Another Generalization of Geometric Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(6), pages 1143-1157, March.
    3. Tomasz Kozubowski & Seidu Inusah, 2006. "A Skew Laplace Distribution on Integers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 555-571, September.
    4. Subrata Chakraborty & Dhrubajyoti Chakravarty, 2016. "A new discrete probability distribution with integer support on (−∞, ∞)," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 492-505, January.
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