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Mixture of Weibull distributions—parametric characterization of failure rate function

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  • R. Jiang
  • D. N. P. Murthy

Abstract

A mixture distribution involving two two‐parameter Weibull distributions is characterized by five parameters. The shape of the failure rate function for the mixture depends on the parameter values and can be one of eight distinct shapes. In this paper we present a complete parametric characterization of the shapes for the failure rate function for the mixture. © 1998 John Wiley & Sons, Ltd.

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  • R. Jiang & D. N. P. Murthy, 1998. "Mixture of Weibull distributions—parametric characterization of failure rate function," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 47-65, March.
    • Handle: RePEc:wly:apsmda:v:14:y:1998:i:1:p:47-65
    DOI: 10.1002/(SICI)1099-0747(199803)14:13.0.CO;2-E
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    Cited by:

    1. Wendy W. Moe & Peter S. Fader, 2002. "Fast-Track: Article Using Advance Purchase Orders to Forecast New Product Sales," Marketing Science, INFORMS, vol. 21(3), pages 347-364, March.
    2. Eshetu T. Wondmagegnehu, 2004. "On the behavior and shape of mixture failure rates from a family of IFR Weibull distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 491-500, June.
    3. Xiaowei Dong & Feng Sun & Fangchao Xu & Qi Zhang & Ran Zhou & Liang Zhang & Zhongwei Liang, 2022. "Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    4. 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.
    5. Peng, Xiuyun & Yan, Zaizai, 2014. "Estimation and application for a new extended Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 34-42.
    6. M Bebbington & C D Lai & D N P Murthy & R Zitikis, 2009. "Modelling N- and W-shaped hazard rate functions without mixing distributions," Journal of Risk and Reliability, , vol. 223(1), pages 59-69, March.
    7. Farcomeni, Alessio & Nardi, Alessandra, 2010. "A two-component Weibull mixture to model early and late mortality in a Bayesian framework," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 416-428, February.
    8. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    9. Baker, Rose, 2019. "New survival distributions that quantify the gain from eliminating flawed components," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 493-501.

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