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Keywords = inverse Bayes formulae

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27 pages, 675 KiB  
Article
Bayesian Inference for the Loss Models via Mixture Priors
by Min Deng and Mostafa S. Aminzadeh
Risks 2023, 11(9), 156; https://doi.org/10.3390/risks11090156 - 31 Aug 2023
Cited by 2 | Viewed by 1694
Abstract
Constructing an accurate model for insurance losses is a challenging task. Researchers have developed various methods to model insurance losses, such as composite models. Composite models combine two distributions: one for part of the data with small and high frequencies and the other [...] Read more.
Constructing an accurate model for insurance losses is a challenging task. Researchers have developed various methods to model insurance losses, such as composite models. Composite models combine two distributions: one for part of the data with small and high frequencies and the other for large values with low frequencies. The purpose of this article is to consider a mixture of prior distributions for exponential–Pareto and inverse-gamma–Pareto composite models. The general formulas for the posterior distribution and the Bayes estimator of the support parameter θ are derived. It is shown that the posterior distribution is a mixture of individual posterior distributions. Analytic results and Bayesian inference based on the proposed mixture prior distribution approach are provided. Simulation studies reveal that the Bayes estimator with a mixture distribution outperforms the Bayes estimator without a mixture distribution and the ML estimator regarding their accuracies. Based on the proposed method, the insurance losses from natural events, such as floods from 2000 to 2019 in the USA, are considered. As a measure of goodness-of-fit, the Bayes factor is used to choose the best-fitted model. Full article
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15 pages, 324 KiB  
Article
Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution
by Fengkai Yang
Symmetry 2023, 15(2), 447; https://doi.org/10.3390/sym15020447 - 8 Feb 2023
Cited by 1 | Viewed by 2386
Abstract
The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative [...] Read more.
The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science)
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