A new extended Fréchet model with different estimation methods and applications.

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The Fréchet distribution is a key model in extreme value theory.
• Existing generalizations of the Fréchet distribution have limitations in flexibility.

Purpose of the Study:

• Introduce a novel statistical model: the new extended Fréchet (NE_Fr) distribution.
• Enhance the flexibility of the classical Fréchet distribution.
• Investigate the mathematical properties and inferential methods for the NE_Fr model.

Main Methods:

• Constructed the NE_Fr model by integrating the new extended X family with the Fréchet distribution.
• Derived key mathematical properties including quantile function, moments, and entropy measures.
• Applied various estimation techniques: maximum likelihood, least squares, and Anderson-Darling estimation.

Main Results:

• The NE_Fr model exhibits flexible probability density function shapes (decreasing, unimodal, right-skewed).
• Its hazard rate function can display decreasing or up-side-down shapes.
• Simulation studies confirmed the computational efficiency of the estimation methods.

Conclusions:

• The NE_Fr distribution provides a more flexible alternative to the standard Fréchet distribution.
• The proposed estimation techniques are computationally efficient and reliable.
• The NE_Fr model demonstrates practical utility through application to real-world datasets.