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Power Burr X-T family of distributions: properties, estimation methods and real-life applications

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  • Rana Muhammad Usman

    (University of the Punjab)

  • Maryam Ilyas

    (University of the Punjab)

Abstract

The new continuous class of probability distribution named the Power Burr X-T (PBX-T) family is proposed in this paper. The essential characteristics of the PBX-T family of distributions, i.e. conventional moments and associated procedures, stress-strength reliability, and Rényi entropy, are derived and studied. Some special models belonging to the new family have been comprehensively explored concerning their shapes. Extensive simulations have been conducted to compare the maximum likelihood (ML) estimates with other classical estimators. It is found that the mean squared errors and the bias of the ML estimates are relatively least for large samples. Moreover, real-life applications from medical and engineering fields have been used to demonstrate the potentiality and adequacy of the suggested sub-models from the PBX-T family. The values of observed goodness-of-fit measures show that the sub-models of the suggested family of distributions are superior in adequacy parallel to the other generalized models.

Suggested Citation

  • Rana Muhammad Usman & Maryam Ilyas, 2024. "Power Burr X-T family of distributions: properties, estimation methods and real-life applications," Computational Statistics, Springer, vol. 39(6), pages 2949-2974, September.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:6:d:10.1007_s00180-023-01405-w
    DOI: 10.1007/s00180-023-01405-w
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    References listed on IDEAS

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    3. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
    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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