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

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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.

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All data used in this research is available and it will be provided on demand.

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  1. University of the Punjab, Lahore, Pakistan

    Rana Muhammad Usman & Maryam Ilyas

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  1. Rana Muhammad Usman
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  2. Maryam Ilyas
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Correspondence to Rana Muhammad Usman.

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Usman, R.M., Ilyas, M. Power Burr X-T family of distributions: properties, estimation methods and real-life applications. Comput Stat 39, 2949–2974 (2024). https://doi.org/10.1007/s00180-023-01405-w

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