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Study on Bayesian Skew-Normal Linear Mixed Model and Its Application in Fire Insurance.

Meiling Gong1, Zhanli Mao1, Di Zhang1

  • 1School of Fire Protection Engineering, China People's Police University, Langfang, China.

Fire Technology
|June 26, 2023
PubMed
Summary

This study introduces a novel skew-normal linear mixed model for fire insurance loss claims. The Bayesian Markov Chain Monte Carlo method effectively addresses data skewness, improving loss claim distribution modeling and insurance rate calculation.

Keywords:
Bayesian MCMC methodFire insurance loss claimOptimizationSkew-normal distribution model

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Area of Science:

  • Actuarial Science
  • Statistical Modeling
  • Risk Management

Background:

  • Fire insurance loss claim data exhibit complex characteristics like skewness and heavy tails.
  • Traditional linear mixed models struggle to accurately capture the distribution of insurance losses.
  • Accurate modeling of loss distributions is critical for effective fire insurance rating.

Purpose of the Study:

  • To develop a scientific and robust distribution model for fire insurance loss claim data.
  • To establish a skew-normal linear mixed model incorporating Bayesian methods.
  • To innovate the calculation of fire insurance premium rates.

Main Methods:

  • Assumed random effects and errors in the linear mixed model follow a skew-normal distribution.
  • Employed the Bayesian Markov Chain Monte Carlo (MCMC) method for model estimation.
  • Utilized the R language JAGS package for posterior distribution analysis and parameter estimation.

Main Results:

  • The proposed Bayesian skew-normal linear mixed model effectively overcomes data skewness.
  • The model demonstrates superior fitting and correlation with sample data compared to the log-normal linear mixed model.
  • Predicted and simulated loss claim values were obtained for rate determination.

Conclusions:

  • The developed distribution model is suitable for describing insurance claims, particularly fire insurance loss data.
  • The Bayesian MCMC approach offers a better fit for skewed and heavy-tailed insurance loss data.
  • This study advances the application of Bayesian methods in fire insurance and offers a new approach for premium rate calculation.