A New Probability Distribution with Applications to ReliefTimes, Fiber Stress and Aircraft Failure Data

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.