Classical and Bayesian estimation for type-I extended-F family with an actuarial application

Area of Science:

• Statistics
• Probability Distributions

Background:

• The need for flexible statistical models is crucial in various fields.
• Existing Weibull-based distributions may not capture complex data patterns adequately.

Purpose of the Study:

• To introduce and analyze the novel type-I extended-F family of distributions.
• To thoroughly investigate the properties and estimation methods for the type-I extended-Weibull (TIEx-W) distribution.
• To assess the TIEx-W distribution's performance and flexibility using real-world insurance data.

Main Methods:

• Derivation of basic properties for the TIEx-W distribution.
• Application of eight classical estimation methods to determine TIEx-W parameters.
• Monte Carlo simulations to evaluate estimator performance for small and large sample sizes.
• Bayesian estimation of parameters using various loss functions on a real dataset.

Main Results:

• The TIEx-W distribution is shown to be a flexible and viable statistical model.
• Performance evaluation of classical and Bayesian estimators for TIEx-W parameters was conducted.
• Analysis of insurance data demonstrated the TIEx-W distribution's superior fit compared to several other Weibull-based models.

Conclusions:

• The proposed TIEx-W distribution offers a flexible and effective alternative for statistical modeling.
• The TIEx-W model provides a better fit for insurance data than competing distributions, highlighting its practical utility.