Insurance loss data are usually in the form of left-truncation and right-censoring due to deductibles and policy limits respectively. This paper investigates the model uncertainty and selection procedure when various parametric models are constructed to accommodate such left-truncated and right-censored data. The joint asymptotic properties of the estimators have been established using the Delta method along with Maximum Likelihood Estimation when the model is specified. We conduct the simulation studies using Fisk, Lognormal, Lomax, Paralogistic, and Weibull distributions with various proportions of loss data below deductibles and above policy limits. A variety of graphic tools, hypothesis tests, and penalized likelihood criteria are employed to validate the models, and their performances on the model selection are evaluated through the probability of each parent distribution being correctly selected. The effectiveness of each tool on model selection is also illustrated using {well-studied} data that represent Wisconsin property losses in the United States from 2007 to 2010.

翻译：保险损失数据通常因免赔额和保单限额而呈现左截断与右删失形式。本文探讨了针对此类左截断与右删失数据构建多种参数模型时的模型不确定性与选择流程。在模型设定条件下，利用Delta方法与极大似然估计法建立了估计量的联合渐近性质。本研究采用Fisk、Lognormal、Lomax、Paralogistic及Weibull分布进行模拟实验，涵盖不同比例的低于免赔额和高于保单限额的损失数据。通过多种图形工具、假设检验及惩罚似然准则验证模型有效性，并基于各母分布被正确选择的概率评估模型选择性能。同时利用2007年至2010年美国威斯康星州财产损失的经充分研究的数据，阐明了各工具在模型选择中的效能。