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.

这项学术工作的主要目的是开发两种估计程序–最大似然估计器（MLE）和微调矩的方法（MTM）–受不同损失控制机制影响的对数正态保险支付严重性数据集的均值和方差，例如，截断（由于自付额），审查（由于保单限额）和缩放（由于共同保险比例），在保险和金融行业。得出了按次付款和按次付款数据集的最大似然估计方程，可以通过任何现有的迭代数值方法轻松求解。这些估计量的渐近分布是通过Fisher信息矩阵建立的。此外，以平衡效率和鲁棒性并消除某些数据点的质量为目标，我们针对上述变换后的数据场景开发了针对对数正态索赔严重性模型的动态MTM估计程序。建立了渐近分布特性，并与那些MTM估计量的相应MLE进行了比较，并进行了广泛的仿真研究。纯粹出于说明目的，提供了1500美国赔偿损失的数值示例，这些示例说明了本文确定结果的实际性能。