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Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

Author

Listed:
  • Sajid Hussain

    (Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan)

  • Mahmood Ul Hassan

    (Department of Statistics, Stockholm University, SE-106 91 Stockholm, Sweden)

  • Muhammad Sajid Rashid

    (Department of Computer Science, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan)

  • Rashid Ahmed

    (Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan)

Abstract

In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions are proposed. The expressions for distribution function and density function of BIIIEE-X family are written in terms of linear combinations of the exponentiated densities based to parent model. New models, i.e., Weibul extended exponentiated Weibull (WEEW), Lomax extended exponentiated Weibull (LEEW), Logistic extended exponentiated Weibull (LGCEEW), and Burr III extended exponentiated-Weibull (BIIIEEW) distributions are derived, were plotted for functions of probability density and hazard rate at different levels of parameters. Some mathematical properties of the BIIIEEW model are disclosed. The maximum likelihood method for the BIIIEEW model are described. Numerical applications of the BIIIEEW model to disease of cancer datasets are provided.

Suggested Citation

  • Sajid Hussain & Mahmood Ul Hassan & Muhammad Sajid Rashid & Rashid Ahmed, 2023. "Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution," Mathematics, MDPI, vol. 11(14), pages 1-24, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3090-:d:1193185
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    References listed on IDEAS

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    1. Sajid Hussain & Muhammad Sajid Rashid & Mahmood Ul Hassan & Rashid Ahmed, 2022. "The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications," Mathematics, MDPI, vol. 10(9), pages 1-19, April.
    2. 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.
    3. Sajid Hussain & Muhammad Sajid Rashid & Mahmood Ul Hassan & Rashid Ahmed, 2022. "The Generalized Exponential Extended Exponentiated Family of Distributions: Theory, Properties, and Applications," Mathematics, MDPI, vol. 10(19), pages 1-22, September.
    4. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    5. Sajid Hussain & Mahmood Ul Hassan & Muhammad Sajid Rashid & Rashid Ahmed, 2023. "The Exponentiated Power Alpha Index Generalized Family of Distributions: Properties and Applications," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
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