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

TL;DR

This paper introduces an adaptive Winsorized Moments method for robustly fitting truncated and censored lognormal distributions, addressing outliers, model robustness, and uncertainty estimation in claims cost prediction.

Contribution

It develops an adaptive Winsorized Moments estimator for truncated and censored lognormal distributions, with theoretical properties and practical validation, improving robustness over existing methods.

Findings

The proposed MWM estimator is robust to outliers.

Theoretical properties of MWM are derived and validated.

Real data application shows comparable performance to simpler models.

Abstract

When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii) parameters should be estimated robustly to control the influence of outliers on model predictions, and (iii) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this paper provides a framework for addressing all 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 sensitivity analysis. Finally, practical performance of these methods is illustrated using the well-studied data set of 1500 U.S. indemnity losses. With this real data set, it is also demonstrated that the composite models do not provide much improvement in the quality of predictive models compared to a stand-alone fitted distribution specially for truncated and censored sample data.