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Probability distributions are very important in describing practical phenomena. Among the available probability distributions, the three-parameter generalized inverse Weibull (for short "GI-Weibull") model has very useful applications in reliability, management, and healthcare studies, among others. This paper considers a weighted adaptation of the proposed new model. We proposed a weighted version of the GI-Weibull distribution, which may be called the weighted generalized inverse Weibull (for short "WGI-Weibull") distribution. The appeal of the WGI-Weibull distribution lies in its altered form of the GI-Weibull distribution, which does not necessitate the incorporation of extra parameters. Various properties of the WGI-Weibull distribution are obtained through mathematical derivation. Finally, a medical application (i.e., a medical data set) is studied and analyzed to illustrate the WGI-Weibull model. A comparison is conducted between the WGI-Weibull distribution and the GI-Weibull and inverse flexible Weibull models utilizing the medical data set. Employing three evaluation metrics, it is shown that the WGI-Weibull model describes the medical phenomena much better than the GI-Weibull and some Weibull models.
AbaOud et al. (2024) studied this question.