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The Weibull Fréchet distribution and its applications

Author

Listed:
  • Ahmed Z. Afify
  • Haitham M. Yousof
  • Gauss M. Cordeiro
  • Edwin M. M. Ortega
  • Zohdy M. Nofal

Abstract

A new four-parameter lifetime model called the Weibull Fréchet distribution is defined and studied. Various of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and $ {\delta } $ δ-entropies and order statistics are investigated. The new density function can be expressed as a linear mixture of Fréchet densities. The maximum likelihood method is used to estimate the model parameters. The new distribution is applied to two real data sets to prove empirically its flexibility. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in many areas.

Suggested Citation

  • Ahmed Z. Afify & Haitham M. Yousof & Gauss M. Cordeiro & Edwin M. M. Ortega & Zohdy M. Nofal, 2016. "The Weibull Fréchet distribution and its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2608-2626, October.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:14:p:2608-2626
    DOI: 10.1080/02664763.2016.1142945
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    References listed on IDEAS

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    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
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    Cited by:

    1. Shanker Rama & Rahman Umme Habibah, 2021. "Type II Topp-Leone Frechet distribution: properties and applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 139-152, December.
    2. Joseph Thomas Eghwerido & Pelumi E. Oguntunde & Friday Ikechukwu Agu, 2023. "The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 172-197, February.
    3. Adebisi Ade Ogunde & Gbenga Adelekan Olalude & Oyebimpe Emmanuel Adeniji & Kayode Balogun, 2021. "Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-8, June.
    4. Rama Shanker & Umme Habibah Rahman, 2021. "Type II Topp-Leone Frechet distribution: properties and applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 139-152, December.
    5. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    6. Joseph Thomas Eghwerido & Lawrence Chukwudumebi Nzei & Friday Ikechukwu Agu, 2021. "The Alpha Power Gompertz Distribution: Characterization, Properties, and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 449-475, February.

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