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

Gareth W. Peters, Wilson Ye Chen and Richard H. Gerlach
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Gareth W. Peters: Department of Statistical Science, University College London, London WC1E 6BT, UK
Wilson Ye Chen: Discipline of Business Analytics, The University of Sydney, Sydney 2006, Australia
Richard H. Gerlach: Discipline of Business Analytics, The University of Sydney, Sydney 2006, Australia

Risks, 2016, vol. 4, issue 2, 1-41

Abstract: This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class of Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterisations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges that are amenable to practitioners when fitting such models is to perform robust estimation of the model parameters. In this paper we develop a novel, efficient, and robust procedure for estimating the parameters of this family of Tukey transform models, based on L-moments. It is shown to be more efficient than the current state of the art estimation methods for such families of loss models while being simple to implement for practical purposes.

Keywords: L-moments; method of moments; quantile distributions; Tukey transformations; g-and-h distribution; g-and-k distribution; tail risk; loss distributions (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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