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<p>In automobile insurance sector, an accurate assessment of claim number and amount plays a pivotal role in calculating insurance premiums based on the policyholder’s level of risk. Within this framework, we introduce a new model called Exponential-Compound Poisson Mixture (ECPM) which generalizes the Compound Poisson one. The elaborated model contributes to the understanding, modeling, and prediction of zero-inflated data. The ECPM regression is used to predict the claim amount <i>S</i> and the Negative Binomial regression to estimate the number of claims <i>N</i>. Under specific hypothesis, the joint probability distribution and the correlation coefficient of (<i>N</i>,&#xa0;<i>S</i>) were derived.</p><p>Based on the maximum likelihood and quasi-likelihood methods, parameters estimation for the proposed ECPM regression model were provided. Simulation studies were carried out to evaluate the asymptotic properties of the obtained estimators. Their corresponding confidence intervals were also deduced through applying the Delta method and the central limit theorem. Experimentally, the application of the proposed model was illustrated using a real data set. In order to prove the performance of this model, it was compared to Gamma and Log-normal models.</p>

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Exponential-compound Poisson mixture model for motor insurance claims

  • 期刊论文

  • 发表日期：

    2025年2月3日

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  • Abdelaziz Ghribi,
  • Chaima Hmani,
  • Afif Masmoudi

摘要

In automobile insurance sector, an accurate assessment of claim number and amount plays a pivotal role in calculating insurance premiums based on the policyholder’s level of risk. Within this framework, we introduce a new model called Exponential-Compound Poisson Mixture (ECPM) which generalizes the Compound Poisson one. The elaborated model contributes to the understanding, modeling, and prediction of zero-inflated data. The ECPM regression is used to predict the claim amount S and the Negative Binomial regression to estimate the number of claims N. Under specific hypothesis, the joint probability distribution and the correlation coefficient of (N, S) were derived.

Based on the maximum likelihood and quasi-likelihood methods, parameters estimation for the proposed ECPM regression model were provided. Simulation studies were carried out to evaluate the asymptotic properties of the obtained estimators. Their corresponding confidence intervals were also deduced through applying the Delta method and the central limit theorem. Experimentally, the application of the proposed model was illustrated using a real data set. In order to prove the performance of this model, it was compared to Gamma and Log-normal models.