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This paper discusses different classes of loss models in non-life insurancesettings. It then overviews the class Tukey transform loss models that have notyet been widely considered in non-life insurance modelling, but offeropportunities to produce flexible skewness and kurtosis features often requiredin loss modelling. In addition, these loss models admit explicit quantilespecifications which make them directly relevant for quantile based riskmeasure calculations. We detail various parameterizations and sub-families ofthe Tukey transform based models, such as the g-and-h, g-and-k and g-and-jmodels, including their properties of relevance to loss modelling.  One of the challenges with such models is to perform robust estimation forthe loss model parameters that will be amenable to practitioners when fittingsuch models. In this paper we develop a novel, efficient and robust estimationprocedure for estimation of model parameters in this family Tukey transformmodels, based on L-moments. It is shown to be more robust and efficient thancurrent state of the art methods of estimation for such families of loss modelsand is simple to implement for practical purposes.

Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments