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在车损险费率厘定中,通常假设索赔频率、索赔强度或纯保费服从指数分布族,并对其均值建立广义线性模型,而假设其他参数对所有风险类别都是固定的常数。这种假设在某些情况下并非成立。GAMLSS模型可以在各种分布假设下同时对一个分布的位置参数、尺度参数和形状参数建立参数或非参数的回归模型,具有很大的灵活性。本文在零调整逆高斯分布假设下把GAMLSS模型应用于我国实际的车损险数据,建立了车损险的费率厘定模型,结果表明,这种模型对车损险实际数据的拟合要优于常用的Tweedie分布假设下的广义线性模型。此外,这种模型厘定的风险保费更加公平合理。
In car damage rate determination, it is usually assumed that the frequency of claims, the strength of claims, or the pure premium are subject to an exponential distribution family, and a generalized linear model of the mean is established, assuming that other parameters are constant for all risk categories. This assumption does not hold in some cases. The GAMLSS model has a great flexibility in establishing a parametric or non-parametric regression model for a distributed position, scale and shape parameters under various distributional assumptions. In this paper, the GAMLSS model is applied to the actual vehicle damage data in our country under the zero-adjusted inverse Gaussian distribution hypothesis, and the rate determination model of the vehicle damage insurance is established. The results show that the model is fit for the actual data of vehicle damage insurance Generalized linear model under the assumption of Tweedie distribution. In addition, the risk premiums determined by this model are more fair and reasonable.