  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.
