By generalizing traditional regression frameworks, generalized additive models for location, scale, and shape (GAMLSSs) allow parametric or semiparametric modeling of one or more parameters of distributions that are not members of the linear exponential family. Consequently, these GAMLSS approaches offer an interesting theoretical framework to allow the use of several potentially helpful distributions in actuarial science. GAMLSS theory is coupled with longitudinal approaches for counting data because these approaches are essential to predictive pricing models. Indeed, they are mainly known for modeling the dependence between the number of claims from the contracts of the same insured over time. Considering that the models’ cross-sectional counterparts have been successfully applied in actuarial work and the importance of longitudinal models, we show that the proposed approach allows one to quickly implement multivariate longitudinal models with nonparametric terms for ratemaking. This semiparametric modeling is illustrated using a dataset from a major insurance company in Canada. An analysis is then conducted on the improvement of predictive power that the use of historical data and nonparametric terms in the modeling allows. In addition, we found that the weight of past experience in bonus–malus predictive premiums analysis is reduced in comparison with a parametric model and that this method could help for continuous covariate segmentation. Our approach differs from previous studies because it does not use any simplifying assumptions as to the value of the a priori explanatory variables and because we have carried out a predictive pricing integrating nonparametric terms within the framework of the GAMLSS in an explicit way, which makes it possible to reproduce the same type of study using other distributions.

通过推广传统的回归框架，位置、尺度和形状的广义加性模型 (GAMLSS) 允许对不属于线性指数族的一个或多个分布参数进行参数或半参数建模。因此，这些 GAMLSS 方法提供了一个有趣的理论框架，允许在精算科学中使用几种可能有用的分布。GAMLSS 理论与纵向数据计数方法相结合，因为这些方法对于预测定价模型至关重要。事实上，它们主要以对同一被保险人的合同索赔数量随时间的依赖性进行建模而闻名。考虑到模型的横截面模型已成功应用于精算工作以及纵向模型的重要性，我们表明，所提出的方法允许人们快速实施具有非参数项的多元纵向模型以进行费率制定。这种半参数建模是使用加拿大一家主要保险公司的数据集进行说明的。然后对建模中使用历史数据和非参数项所允许的预测能力的提高进行分析。此外，我们发现，与参数模型相比，奖金-恶意预测保费分析中过去经验的权重有所降低，并且该方法有助于连续协变量分割。