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A general class of flexible Weibull distributions

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  • Sangun Park
  • Jiwhan Park

Abstract

We consider a linear combination of two logarithms of cumulative hazard functions and propose a general class of flexible Weibull distribution functions which includes some well-known modified Weibull distributions (MWDs). We suggest a very flexible Weibull distribution, which belongs to the class, and show that its hazard function is monotone, bathtub-shaped, modified bathtub-shaped, or even upside-down bathtub-shaped. We also discuss the methods of least square estimation and maximum likelihood estimation of the unknown parameters. We take two illustrated examples to compare the suggested distribution with some current MWDs, and show that the suggested distribution shows good performances.

Suggested Citation

  • Sangun Park & Jiwhan Park, 2018. "A general class of flexible Weibull distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(4), pages 767-778, February.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:4:p:767-778
    DOI: 10.1080/03610926.2015.1118509
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    Cited by:

    1. Abdoulaye Diamoutene & Farid Noureddine & Rachid Noureddine & Bernard Kamsu-Foguem & Diakarya Barro, 2020. "Proportional hazard model for cutting tool recovery in machining," Journal of Risk and Reliability, , vol. 234(2), pages 322-332, April.
    2. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.

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