Modified Weibull-Fréchet Distribution Properties with Application

In this paper, we develop new statistical distribution from within the continuous distributions based on the Hybrid Weibull-G family and the Frechet distribution, called the Hybrid Weibull Frechet. This development comes by adding two new parameters to the basic distributions to give more flexibility and suitability to the basic Frechet distribution for reading and modeling real-world data. Also, present the basic functions of the new distribution (PDF, CDF). In addition, the paper will present an expansion of these functions and an expansion of the powers on which many statistical properties of the two proposed distributions will be built, such as the moments function, Incomplete Moments, Probability Weighted Moments, the survival function, the quantity function, and four types of entropy and disparity measures that represent a small number of... Numerous mathematical and statistical features of the developed distribution. The parameters were also estimated using the MLE. To obtain a distribution characterized by high flexibility to match different types of real data, a simulation was conducted to demonstrate the efficiency of estimating the unknown parameters of the new distribution using the maximum likelihood method. In addition, each distribution was tested on two types of real data of different sizes. The proposed new distribution proved highly flexible for the data when compared to other distributions using some statistical standards such as AIC, BIC, CAIC, and HQIC. The results showed the extent of flexibility and accuracy that supports what was discussed in the theoretical aspect.