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

• DOI: 10.1371/journal.pone.0275430
• Publication Date: 2023-02-02T19:16:28Z
• Authors: Nada M. Alfaer; Sarah A. Bandar; Omid Kharazmi; Hazem Al-Mofleh; Zubair Ahmad; Ahmed Z. Afify
• Keywords: Statistics and Probability; Economics; Science; Social Sciences; Management Science and Operations Research; Bayesian probability; 01 natural sciences; Decision Sciences; FOS: Economics and business; Bayes' theorem; Methods for Handling Missing Data in Statistical Analysis; Skew Distributions and Applications in Statistics; FOS: Mathematics; Computer Simulation; Econometrics; 0101 mathematics; Modeling Risk in Insurance and Finance; Biology; Likelihood Functions; Ecology; Q; Statistics; R; Mixed-Effects Models; Bayes Theorem; Applied mathematics; Computer science; Management; FOS: Biological sciences; Physical Sciences; Medicine; Monte Carlo Method; Type (biology); Estimation; Mathematics; Research Article; Statistical Distributions

In this work, a new flexible class, called the type-I extended- F family, is proposed. A special sub-model of proposed extended-Weibull (TIEx-W) distribution, explored in detail. Basic properties TIEx-W distribution are provided. The parameters obtained by eight classical methods estimation. performance these estimators using Monte Carlo simulation results for small and large samples. Besides, Bayesian estimation model under different loss functions real data set also importance flexibility illustrated analyzing an insurance data. real-life illustrates that provides better fit as compared to competing models such Lindley–Weibull, exponentiated Weibull, Kumaraswamy–Weibull, α logarithmic transformed beta Weibull distributions, among others.