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A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data

Author

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  • Gauss M. Cordeiro

    (Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil)

  • Elisângela C. Biazatti

    (Department of Mathematics and Statistics, Federal University of Rondônia, Ji-Paraná 76900-726, Brazil)

  • Luís H. de Santana

    (Department of Technology, State University of Maringá, Umuarama 87506-370, Brazil)

Abstract

The Weibull is a popular distribution that models monotonous failure rate data. In this work, we introduce the four-parameter Weibull extended Weibull distribution that presents greater flexibility, thus modeling data with bathtub-shaped and unimodal failure rate. Some of its mathematical properties such as quantile function, linear representation and moments are provided. The maximum likelihood estimation is adopted to estimate its parameters, and the log-Weibull extended Weibull regression model is presented. In addition, some simulations are carried out to show the consistency of the estimators. We prove the greater flexibility and performance of this distribution and the regression model through applications to influenza and hepatitis data. The new models perform much better than some of their competitors.

Suggested Citation

  • Gauss M. Cordeiro & Elisângela C. Biazatti & Luís H. de Santana, 2023. "A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data," Stats, MDPI, vol. 6(2), pages 1-17, May.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:2:p:42-673:d:1151163
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    References listed on IDEAS

    as
    1. Monica A Konerman & Lauren A Beste & Tony Van & Boang Liu & Xuefei Zhang & Ji Zhu & Sameer D Saini & Grace L Su & Brahmajee K Nallamothu & George N Ioannou & Akbar K Waljee, 2019. "Machine learning models to predict disease progression among veterans with hepatitis C virus," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-14, January.
    2. Gauss Cordeiro & Saralees Nadarajah & Edwin Ortega, 2012. "The Kumaraswamy Gumbel distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 139-168, June.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    5. Edwin Ortega & Gauss Cordeiro & Michael Kattan, 2013. "The log-beta Weibull regression model with application to predict recurrence of prostate cancer," Statistical Papers, Springer, vol. 54(1), pages 113-132, February.
    6. M. H. Tahir & Gauss M. Cordeiro & M. Mansoor & M. Zubair & Morad Alizadeh, 2016. "The Weibull–Dagum distribution: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7376-7398, December.
    7. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
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