A new generator for proposing flexible lifetime distributions and its properties

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Continuous lifetime distributions are fundamental in various scientific fields.
• Existing distributions may lack the flexibility to accurately model complex data.
• There is a need for adaptable statistical models in survival analysis.

Purpose of the Study:

• To develop a novel generator for creating new continuous lifetime distributions.
• To enhance the flexibility of existing lifetime distributions through a simple parameter transformation.
• To demonstrate the practical utility and superiority of the proposed generator.

Main Methods:

• A generator is developed using a transformation with an additional parameter.
• Stochastic properties of the new distributions are derived.
• Parameter estimation is performed using maximum likelihood for complete and censored data (Type-I, Type-II, random censoring).
• Monte Carlo simulations are used to assess estimator consistency.

Main Results:

• The proposed generator successfully creates more flexible lifetime distributions.
• Maximum likelihood estimators are shown to be consistent via simulation.
• An extended Fréchet distribution is presented as a practical example.
• The new approach outperforms existing extensions of the Fréchet distribution in real-world applications.

Conclusions:

• The proposed generator provides a powerful tool for developing flexible lifetime distributions.
• The method is effective for parameter estimation with various censoring schemes.
• The enhanced Fréchet distribution demonstrates significant improvements over existing models, highlighting the generator's practical value.