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On the Additive Weibull Distribution

Author

Listed:
  • Artur J. Lemonte
  • Gauss M. Cordeiro
  • Edwin M. M. Ortega

Abstract

We derive explicit expressions for the moments, incomplete moments, quantile function and generating function of the additive Weibull model pioneered by Xie and Lai (1995), which is a quite flexible distribution for fitting lifetime data with bathtub-shaped failure rate function. In addition, we estimate the model parameters by maximum likelihood and determine the observed information matrix. The flexibility of the additive Weibull distribution is illustrated by means of one application to real data.

Suggested Citation

  • Artur J. Lemonte & Gauss M. Cordeiro & Edwin M. M. Ortega, 2014. "On the Additive Weibull Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2066-2080, May.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2066-2080
    DOI: 10.1080/03610926.2013.766343
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    Cited by:

    1. Emrah Altun & Mustafa Ç. Korkmaz & Mahmoud El-Morshedy & Mohamed S. Eliwa, 2021. "A New Flexible Family of Continuous Distributions: The Additive Odd-G Family," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    2. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Zeng, Hongtao & Lan, Tian & Chen, Qiming, 2016. "Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 307-315.
    4. Trevor Fenner & Mark Levene & George Loizou, 2018. "A multiplicative process for generating the rank-order distribution of UK election results," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(3), pages 1069-1079, May.
    5. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    6. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.

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