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A New Extension of Weibull Distribution with Application to Lifetime Data

Author

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  • Sanku Dey

    (King Abdulaziz University)

  • Vikas Kumar Sharma

    (Institute of Infrastructure, Technology, Research and Management (IITRAM))

  • Mhamed Mesfioui

    (King Abdulaziz University
    Université du Québec à Trois-Rivières)

Abstract

The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization, called alpha-power transformed Weibull distribution that provides better fits than the Weibull distribution and some of its known generalizations. The distribution contains alpha-power transformed exponential and alpha-power transformed Rayleigh distributions as special cases. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress–strength reliability and order statistics are derived. The distribution is capable of modeling monotonically increasing, decreasing, constant, bathtub, upside-down bathtub and increasing–decreasing–increasing hazard rates. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Two data sets have been analyzed to show how the proposed models work in practice. Further, a bivariate extension based on Marshall–Olkin and copula concept of the proposed model are developed but the properties of the distribution not considered in detail in this paper that can be addressed in future research.

Suggested Citation

  • Sanku Dey & Vikas Kumar Sharma & Mhamed Mesfioui, 2017. "A New Extension of Weibull Distribution with Application to Lifetime Data," Annals of Data Science, Springer, vol. 4(1), pages 31-61, March.
    • Handle: RePEc:spr:aodasc:v:4:y:2017:i:1:d:10.1007_s40745-016-0094-8
    DOI: 10.1007/s40745-016-0094-8
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    Cited by:

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    2. Pramendra Singh Pundir & Puneet Kumar Gupta, 2018. "Reliability Estimation in Load-Sharing System Model with Application to Real Data," Annals of Data Science, Springer, vol. 5(1), pages 69-91, March.
    3. Hiba Zeyada Muhammed, 2023. "A Class of Bivariate Modified Weighted Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 10(4), pages 875-906, August.
    4. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.
    5. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    6. Shumaila Ihtisham & Alamgir Khalil & Sadaf Manzoor & Sajjad Ahmad Khan & Amjad Ali, 2019. "Alpha-Power Pareto distribution: Its properties and applications," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-15, June.
    7. Wei Zhao & Saima K Khosa & Zubair Ahmad & Muhammad Aslam & Ahmed Z Afify, 2020. "Type-I heavy tailed family with applications in medicine, engineering and insurance," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
    8. Ateq Alghamedi & Sanku Dey & Devendra Kumar & Saeed A. Dobbah, 2020. "A New Extension of Extended Exponential Distribution with Applications," Annals of Data Science, Springer, vol. 7(1), pages 139-162, March.
    9. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.
    10. Zubair Ahmad & M. Elgarhy & G. G. Hamedani, 2018. "A new Weibull-X family of distributions: properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-18, December.
    11. 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.

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