On the Extended Generalized Inverted Kumaraswamy Distribution

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The development of flexible statistical distributions is crucial for accurately modeling complex data.
• Existing generalized distributions may not capture the full range of behaviors observed in lifetime data.

Purpose of the Study:

• To introduce a novel, flexible class of probability distributions: the extended generalized inverted Kumaraswamy generated (EGIKw-G) family.
• To derive and analyze the key structural properties of this new distribution family.
• To demonstrate the utility and superiority of a specific model within this family (EGIKw-Burr XII) for lifetime data analysis.

Main Methods:

• Mathematical derivation of structural properties including survival function, hazard rate function, quantile function, and moments.
• Parameter estimation using the maximum likelihood estimation (MLE) method.
• Model performance evaluation through Monte Carlo simulations (MCS).

Main Results:

• The EGIKw-G family of distributions is mathematically defined and its properties are derived.
• The extended generalized inverted Kumaraswamy Burr XII (EGIKw-Burr XII) model is presented as a key special case.
• Simulation studies and real-world data application confirm the effectiveness and superiority of the EGIKw-Burr XII model.

Conclusions:

• The proposed EGIKw-G family offers a valuable addition to the toolkit of statistical distributions.
• The EGIKw-Burr XII model demonstrates strong performance in modeling lifetime data, outperforming existing models.
• This research provides a robust framework for statistical modeling in various applied fields.