The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.

翻译：本学术工作的主要目标是针对保险与金融行业中受不同损失控制机制（例如截断（由免赔额引起）、删失（由保单限额引起）以及缩放（由共保比例引起））影响的对数正态保险赔付严重性数据集，开发两种估计方法——最大似然估计（MLE）与截尾矩估计法（MTM）。推导出了适用于逐次赔付与逐次损失数据集的最大似然估计方程，这些方程可通过任何现有的迭代数值方法轻松求解。通过Fisher信息矩阵建立了这些估计量的渐近分布。此外，为平衡效率与稳健性并消除某些数据点的点质量，本文针对上述变换数据场景，开发了对数正态索赔严重性模型的动态截尾矩估计法。在广泛的模拟研究基础上，建立了这些截尾矩估计量的渐近分布性质，并将其与相应的最大似然估计进行了比较。纯为说明目的，本文提供了1500个美国赔偿损失的数值示例，以展示所建立结果的实际性能。