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Risks 2017, 5(4), 60; doi:10.3390/risks5040060

An EM Algorithm for Double-Pareto-Lognormal Generalized Linear Model Applied to Heavy-Tailed Insurance Claims

Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne, VIC 3010, Australia
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Received: 27 September 2017 / Revised: 2 November 2017 / Accepted: 3 November 2017 / Published: 7 November 2017
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Abstract

Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM algorithm for the heavy-tailed Double-Pareto-lognormal generalized linear model. The DPLN distribution is obtained as a mixture of a lognormal distribution with a double Pareto distribution. In this paper the associated generalized linear model has the location parameter equal to a linear predictor which is used to model insurance claim amounts for various data sets. The performance is compared with those of the generalized beta (of the second kind) and lognorma distributions. View Full-Text
Keywords: insurance claim; double Pareto lognormal distribution; heavy-tailed; generalized beta distribution of the second kind; EM algorithm insurance claim; double Pareto lognormal distribution; heavy-tailed; generalized beta distribution of the second kind; EM algorithm
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Calderín-Ojeda, E.; Fergusson, K.; Wu, X. An EM Algorithm for Double-Pareto-Lognormal Generalized Linear Model Applied to Heavy-Tailed Insurance Claims. Risks 2017, 5, 60.

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