IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i2d10.1007_s11009-019-09731-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09731-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-019-09731-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    2. Eric M. Aldrich & Daniel Friedman, 2023. "Order Protection Through Delayed Messaging," Management Science, INFORMS, vol. 69(2), pages 774-790, February.
    3. Kosto Mitov & Saralees Nadarajah, 2023. "Entropy of Some Discrete Distributions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-19, March.
    4. Sugata Ghosh & Subhajit Dutta & Marc G. Genton, 2017. "A note on inconsistent families of discrete multivariate distributions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.
    5. 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.
    6. Marco Capasso & Elena Cefis & Alessandro Sapio, 2013. "Reconciling quantile autoregressions of firm size and variance–size scaling," Small Business Economics, Springer, vol. 41(3), pages 609-632, October.
    7. Joost Berkhout & Bernd Heidergott & Jennifer Sommer & Hans Daduna, 2019. "Robustness analysis of generalized Jackson network," Computational Management Science, Springer, vol. 16(4), pages 697-714, October.
    8. Alessandro Barbiero, 2022. "Discrete analogues of continuous bivariate probability distributions," Annals of Operations Research, Springer, vol. 312(1), pages 23-43, May.
    9. Wagner Barreto-Souza & Marcelo Bourguignon, 2015. "A skew INAR(1) process on $${\mathbb {Z}}$$ Z," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 189-208, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09731-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.