In this article, a new flexible statistical model is developed, known as the Khalil New Generalized Fréchet (KNG-Fréchet) distribution, which extends the classical Fréchet distribution to better capture complex data behaviors. Several statistical properties of the proposed distribution, including its quantile function, moments, moment generating function, and characteristic function, are thoroughly explored. Parameter estimation is performed using the maximum likelihood estimation (MLE) method. A simulation study is conducted to evaluate the performance of the MLEs in terms of bias and mean squared error (MSE). To validate the effectiveness of the proposed distribution in real-world scenarios, the proposed distribution is applied to three real-life datasets and compared with existing models using goodness-of-fit criteria. The results demonstrate that the proposed model provides a good fit compared to existing alternative distributions, consistently outperforming them in terms of goodness-of-fit measures, parameter stability, and overall flexibility when applied to different datasets and sample sizes.
Osama et al. (Tue,) studied this question.