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Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Author

Listed:
  • M. El-Morshedy

    (Department of Mathematics, College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Ziyad Ali Alhussain

    (Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia)

  • Doaa Atta

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51482, Saudi Arabia)

  • Ehab M. Almetwally

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

  • M. S. Eliwa

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

Suggested Citation

  • M. El-Morshedy & Ziyad Ali Alhussain & Doaa Atta & Ehab M. Almetwally & M. S. Eliwa, 2020. "Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:264-:d:321549
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    References listed on IDEAS

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    1. M. S. Eliwa & M. El-Morshedy, 2019. "Bivariate Gumbel-G Family of Distributions: Statistical Properties, Bayesian and Non-Bayesian Estimation with Application," Annals of Data Science, Springer, vol. 6(1), pages 39-60, March.
    2. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    3. Balakrishnan, Narayanaswamy & Ristić, Miroslav M., 2016. "Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 194-207.
    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. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
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    Cited by:

    1. Hanan Haj Ahmad & Ehab M. Almetwally & Dina A. Ramadan, 2023. "Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach," Mathematics, MDPI, vol. 11(9), pages 1-23, May.
    2. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    3. El-Sayed A. El-Sherpieny & Ehab M. Almetwally & Hiba Z. Muhammed, 2023. "Bayesian and Non-Bayesian Estimation for the Parameter of Bivariate Generalized Rayleigh Distribution Based on Clayton Copula under Progressive Type-II Censoring with Random Removal," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1205-1242, August.

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