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Estimating turning points of the failure rate of the extended Weibull distribution

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  • Gupta, Ramesh C.
  • Lvin, Sergey
  • Peng, Cheng

Abstract

Marshall and Olkin (1997) proposed a way of introducing a parameter, called the tilt parameter, to expand a family of distributions. In this paper we compare the extended distribution and the original distribution with respect to some stochastic orderings. Also we investigate thoroughly the monotonicity of the failure rate of the resulting distribution when the baseline distribution is taken as Weibull. It turns out that the failure rate is increasing, decreasing, or non-monotonic with one or two turning points depending on the parameters. For non-monotonic types, the turning points of the failure rate are estimated and their confidence intervals are provided. Simulation studies are carried out to examine the performance of these intervals. An example is provided to illustrate the procedure.

Suggested Citation

  • Gupta, Ramesh C. & Lvin, Sergey & Peng, Cheng, 2010. "Estimating turning points of the failure rate of the extended Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 924-934, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:924-934
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    References listed on IDEAS

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    1. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
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    1. Nanda, Asok K. & Das, Suchismita, 2012. "Stochastic orders of the Marshall–Olkin extended distribution," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 295-302.
    2. Diren Yeğen & Gamze Özel, 2018. "Marshall-Olkin Half Logistic Distribution with Theory and Applications," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 6(2), pages 407-416, December.
    3. 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.
    4. Narayanaswamy Balakrishnan & Ghobad Barmalzan & Abedin Haidari, 2018. "Ordering Results for Order Statistics from Two Heterogeneous Marshall-Olkin Generalized Exponential Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 292-304, November.

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