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Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data

Author

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  • Refah Alotaibi

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

  • Lamya A. Baharith

    (Department of Statistics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ehab M. Almetwally

    (Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt
    Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo 12613, Egypt
    The Scientific Association for Studies and Applied Research, Al Manzalah 35646, Egypt)

  • Mervat Khalifa

    (Department of Statistics, Al-Azhar University, Cairo 11751, Egypt)

  • Indranil Ghosh

    (Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC 27599, USA)

  • Hoda Rezk

    (Department of Statistics, Al-Azhar University, Cairo 11751, Egypt)

Abstract

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models.

Suggested Citation

  • Refah Alotaibi & Lamya A. Baharith & Ehab M. Almetwally & Mervat Khalifa & Indranil Ghosh & Hoda Rezk, 2022. "Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data," Mathematics, MDPI, vol. 10(15), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2800-:d:882333
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    References listed on IDEAS

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    1. Nadarajah, Saralees & Rocha, Ricardo, 2016. "Newdistns: An R Package for New Families of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i10).
    2. Refah Alotaibi & Ehab M. Almetwally & Indranil Ghosh & Hoda Rezk, 2022. "Classical and Bayesian Inference on Finite Mixture of Exponentiated Kumaraswamy Gompertz and Exponentiated Kumaraswamy Fréchet Distributions under Progressive Type II Censoring with Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    3. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
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