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Risks 2016, 4(2), 14; doi:10.3390/risks4020014

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

1
Department of Statistical Science, University College London, London WC1E 6BT, UK
2
Oxford-Man Institute, Oxford University, Oxford OX2 6ED, UK
3
System Risk Center, London School of Economics, London WC2A 2AE, UK
4
Discipline of Business Analytics, The University of Sydney, Sydney 2006, Australia
*
Author to whom correspondence should be addressed.
Academic Editor: Montserrat Guillén
Received: 28 February 2016 / Revised: 19 April 2016 / Accepted: 2 May 2016 / Published: 20 May 2016
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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. View Full-Text
Keywords: L-moments; method of moments; quantile distributions; Tukey transformations; g-and-h distribution; g-and-k distribution; tail risk; loss distributions L-moments; method of moments; quantile distributions; Tukey transformations; g-and-h distribution; g-and-k distribution; tail risk; loss distributions
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Peters, G.W.; Chen, W.Y.; Gerlach, R.H. Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments. Risks 2016, 4, 14.

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