IDEAS home Printed from https://ideas.repec.org/a/spr/jstada/v5y2018i1d10.1186_s40488-017-0082-3.html
   My bibliography  Save this article

The power-Cauchy negative-binomial: properties and regression

Author

Listed:
  • Muhammad Zubair

    (Department of Statistics, Govt. S.E. College, Bahawalpur, Pakistan)

  • Muhammad H. Tahir

    (The Islamia University of Bahawalpur)

  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco)

  • Ayman Alzaatreh

    (American University of Sharjah)

  • Edwin M. M. Ortega

    (Universidade de São Paulo)

Abstract

We propose and study a new compounded model to extend the half-Cauchy and power-Cauchy distributions, which offers more flexibility in modeling lifetime data. The proposed model is analytically tractable and can be used effectively to analyze censored and uncensored data sets. Its density function can have various shapes such as reversed-J and right-skewed. It can accommodate different hazard shapes such as decreasing, upside-down bathtub and decreasing-increasing-decreasing. Some mathematical properties of the new distribution can be determined from a linear combination for its density function such as ordinary and incomplete moments. The performance of the maximum likelihood method to estimate the model parameters is investigated by a simulation study. Further, we introduce the new log-power-Cauchy negative-binomial regression model for censored data, which includes as sub-models some widely known regression models that can be applied to censored data. Four real life data sets, of which one is censored, have been analyzed and the new models provide adequate fits.

Suggested Citation

  • Muhammad Zubair & Muhammad H. Tahir & Gauss M. Cordeiro & Ayman Alzaatreh & Edwin M. M. Ortega, 2018. "The power-Cauchy negative-binomial: properties and regression," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-17, December.
    • Handle: RePEc:spr:jstada:v:5:y:2018:i:1:d:10.1186_s40488-017-0082-3
    DOI: 10.1186/s40488-017-0082-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40488-017-0082-3
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40488-017-0082-3?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
    ---><---

    References listed on IDEAS

    as
    1. Vahid Nekoukhou & Hamid Bidram, 2017. "A new generalization of the Weibull-geometric distribution with bathtub failure rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(9), pages 4296-4310, May.
    2. Beatriz R. Lanjoni & Edwin M. M. Ortega & Gauss M. Cordeiro, 2016. "Extended Burr XII Regression Models: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 203-224, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Naif Alotaibi & Ibrahim Elbatal & Ehab M. Almetwally & Salem A. Alyami & A. S. Al-Moisheer & Mohammed Elgarhy, 2022. "Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data," Mathematics, MDPI, vol. 10(9), pages 1-25, May.

    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. Thiago G. Ramires & Niel Hens & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model," Computational Statistics, Springer, vol. 33(2), pages 709-730, June.

    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:jstada:v:5:y:2018:i:1:d:10.1186_s40488-017-0082-3. 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.