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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    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.

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