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

Nada M Alfaer1, Sarah A Bandar2, Omid Kharazmi3

  • 1Department of Mathematics & Statistics, College of Science, Taif University, Taif, Saudi Arabia.

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Summary

A new flexible statistical model, the type-I extended-Weibull (TIEx-W) distribution, is introduced. This model demonstrates superior performance in fitting real-world insurance data compared to existing distributions.

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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.