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The Exponentiated Power Alpha Index Generalized Family of Distributions: Properties and Applications

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

The study of hydrological characteristics has a vital role in designing, planning, and managing water resources. The selection of appropriate probability distributions and methods of estimations are basic elements in hydrology analyses. In this article, a new family named the ‘exponentiated power alpha index generalized’ (EPAIG)-G is proposed to develop several new distributions. Using this proposed family, we developed a new model, called the EPAIG-exponential (EPAIG-E). A few structural properties of the EPAIG-G were obtained. The EPAIG-E parameters were estimated through the method of maximum likelihood (MML). The study of the Monte Carlo simulation (MCS) was produced for the EPAIG-E. The model performance is illustrated using real data.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:900-:d:1064200
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    References listed on IDEAS

    as
    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. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    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.
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    1. 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.

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