Method of Winsorized Moments for Robust Fitting of Truncated and Censored Lognormal Distributions

Abstract

When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (1) models should be designed to accommodate deductibles, policy limits, and coinsurance factors; (2) parameters should be estimated robustly to control the influence of outliers on model predictions; and (3) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this article provides a framework for addressing all of these aspects simultaneously. Using payment per payment and payment per loss variables, we construct the adaptive version of method of winsorized moments (MWM) estimators for the parameters of truncated and censored lognormal distribution. Further, the asymptotic distributional properties of this approach are derived and compared with those of the maximum likelihood estimator (MLE) and method of trimmed moments (MTM) estimators, the latter being a primary competitor to MWM. Moreover, the theoretical results are validated with extensive simulation studies and risk measure robustness analysis. Finally, practical performance of these methods is illustrated using the well-studied dataset of 1500 U.S. indemnity losses.