A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data.

Area of Science:

• Statistics
• Probability Theory
• Extreme Value Theory

Background:

• Extreme events pose significant societal and scientific challenges.
• Traditional probability distributions often fail to adequately model clustered extreme observations.
• There is a need for flexible distributions to analyze extreme value data across various fields.

Purpose of the Study:

• To introduce a new, flexible probability distribution for modeling extreme events.
• To derive the distributional properties of the proposed model.
• To demonstrate the model's utility with real-world extreme value data.

Main Methods:

• The new distribution is developed by combining the flexible Weibull distribution with the weighted T-X (Transformed-X) strategy.
• Distributional properties of the new model are mathematically derived.
• Estimation methods are explored for the parameters of the new distribution.

Main Results:

• A novel probability distribution, the flexible Weibull extension distribution, has been successfully developed.
• The mathematical properties of this new distribution have been established.
• The application of estimation techniques for the new model has been investigated.

Conclusions:

• The flexible Weibull extension distribution offers a valuable new tool for analyzing extreme value data.
• This distribution is applicable to diverse fields including finance, hydrology, and meteorology.
• The study demonstrates the practical utility of the proposed distribution through data analysis.