An Enhanced Fréchet Distribution : Properties, Computational Methods and Applications in Cancer Survival and Material Strength

Abstract

This study is devoted to the development of the Enhancing Fréchet distribution (EF) through the integration of hybrid Weibull-G (HWG) family with Fréchet distribution. The resulting EF model demonstrates greater flexibility in modelling datasets characterized by heavy tails and pronounced positive skewness. A comprehensive investigation of its statistical properties is conducted. As verified by the graphs of the different functions, which showed a variety of shapes depending on parameter values. Moments, variance, skewness, and kurtosis were also calculated, confirming the presence of heavy tails and strong positive skewness in EF distribution. In addition, the parameters EF distribution was estimated employing different methods, followed by a simulation that showed that the MLE method was the most accurate and least biased compared to the other methods, especially with increasing sample size. On the applied side, the performance of the new distribution was tested on two real data sets where it yielded the lowest values for information criteria and the highest p-values, confirming its high fit to the data.