  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.
