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Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test

Author

Listed:
  • Muhammad Ahsan ul Haq

    (University of the Punjab
    National College of Arts)

  • Sharqa Hashmi

    (University of the Punjab
    Lahore College for Women University (LCWU))

  • Khaoula Aidi

    (University Badji Mokhtar)

  • Pedro Luiz Ramos

    (University of São Paulo)

  • Francisco Louzada

    (University of São Paulo)

Abstract

In this paper, a new three-parameter unit probability distribution is proposed. The new model is a generalization of Burr III distribution, and it is more flexible than some existing well-known distribution due to its different shapes of the hazard function and probability density functions. The mathematical properties of this distribution are presented, including moments, reliability measures, mean residual life, and characterizations, and we also propose a modified Chi squared goodness-of-fit test based on Nikulin–Rao–Robson statistic Y2 in the presence of complete and censored data. The parameters related to the proposed distribution are estimated using well-known estimation methods. A numerical simulations study is conducted for reinforcement of the results. In the end, we considered two real datasets to illustrate the applicability of the proposed model.

Suggested Citation

  • Muhammad Ahsan ul Haq & Sharqa Hashmi & Khaoula Aidi & Pedro Luiz Ramos & Francisco Louzada, 2023. "Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test," Annals of Data Science, Springer, vol. 10(2), pages 415-440, April.
    • Handle: RePEc:spr:aodasc:v:10:y:2023:i:2:d:10.1007_s40745-020-00298-6
    DOI: 10.1007/s40745-020-00298-6
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    References listed on IDEAS

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    1. Subrata Chakraborty & Laba Handique & Rana Muhammad Usman, 2020. "A Simple Extension of Burr-III Distribution and Its Advantages over Existing Ones in Modelling Failure Time Data," Annals of Data Science, Springer, vol. 7(1), pages 17-31, March.
    2. M. E. Ghitany & J. Mazucheli & A. F. B. Menezes & F. Alqallaf, 2019. "The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3423-3438, July.
    3. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    4. Rana Muhammad Usman & Muhammad Ahsan ul Haq, 2019. "Some Remarks on Odd Burr III Weibull Distribution," Annals of Data Science, Springer, vol. 6(1), pages 21-38, March.
    5. Josmar Mazucheli & André Felipe Menezes & Sanku Dey, 2019. "Unit-Gompertz Distribution with Applications," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 25-43.
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