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

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