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A new generalized weighted Weibull distribution with decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate

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  • Filippo Domma
  • Francesca Condino
  • Božidar V. Popović

Abstract

Recently, Domma et al. [An extension of Azzalinis method, J. Comput. Appl. Math. 278 (2015), pp. 37–47] proposed an extension of Azzalini's method. This method can attract readers due to its flexibility and ease of applicability. Most of the weighted Weibull models that have been introduced are with monotonic hazard rate function. This fact limits their applicability. So, our aim is to build a new weighted Weibull distribution with monotonic and non-monotonic hazard rate function. A new weighted Weibull distribution, so-called generalized weighted Weibull (GWW) distribution, is introduced by a method exposed in Domma et al. [13]. GWW distribution possesses decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate. Also, it is very easy to derive statistical properties of the GWW distribution. Finally, we consider application of the GWW model on a real data set, providing simulation study too.

Suggested Citation

  • Filippo Domma & Francesca Condino & Božidar V. Popović, 2017. "A new generalized weighted Weibull distribution with decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2978-2993, December.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:16:p:2978-2993
    DOI: 10.1080/02664763.2016.1267118
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.
    2. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    3. 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.
    4. Bo Bergman & Bengt Klefsjö, 1984. "The Total Time on Test Concept and Its Use in Reliability Theory," Operations Research, INFORMS, vol. 32(3), pages 596-606, June.
    5. Zhang, Tieling & Dwight, Richard, 2013. "Choosing an optimal model for failure data analysis by graphical approach," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 111-123.
    6. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
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    Cited by:

    1. Célestin C. Kokonendji & Aboubacar Y. Touré & Rahma Abid, 2022. "On General Exponential Weight Functions and Variation Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 924-940, August.
    2. Freddy Hernández & Viviana Giampaoli, 2018. "The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model," Stats, MDPI, vol. 1(1), pages 1-29, May.
    3. Božidar V. Popović & Ali İ. Genç & Filippo Domma, 2022. "Generalized proportional reversed hazard rate distributions with application in medicine," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 459-480, September.

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