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On the moments of the modified Weibull distribution

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  • Nadarajah, Saralees

Abstract

In a recent paper, Xie et al. [Reliab Eng Syst Saf 2002;76:279–85] proposed a modification of the Weibull distribution to allow it to exhibit bathtub-shaped failure rate functions. In this note, we derive explicit algebraic formulas for the kth moment of the distribution. The formulas allow one to calculate the moments for a wide range of values of k and the shape parameter of the modified Weibull. They also allow one to calculate the moments more easily with less computational time. Besides being of interest in their own, we believe that these formulas will be useful for any follow-up mathematical study of the proposed distribution.

Suggested Citation

  • Nadarajah, Saralees, 2005. "On the moments of the modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 114-117.
    • Handle: RePEc:eee:reensy:v:90:y:2005:i:1:p:114-117
    DOI: 10.1016/j.ress.2004.09.002
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    Cited by:

    1. 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.
    2. Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Ahmed, Essam A., 2012. "Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 48-57.
    3. 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.
    4. Silva, Giovana O. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2009. "A log-extended Weibull regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4482-4489, October.
    5. Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.
    6. Zhang, L.F. & Xie, M. & Tang, L.C., 2007. "A study of two estimation approaches for parameters of Weibull distribution based on WPP," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 360-368.
    7. Elbatal I., 2011. "Exponentiated Modified Weibull Distribution," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 189-200, January.

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