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mvClaim: an R package for multivariate general insurance claims severity modelling

Published online by Cambridge University Press:  05 April 2021

Sen Hu ,
T. Brendan Murphy  and
Adrian O’Hagan
Sen Hu*
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland Insight Centre for Data Analytics, University College Dublin, Dublin 4, Ireland
T. Brendan Murphy
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland Insight Centre for Data Analytics, University College Dublin, Dublin 4, Ireland
Adrian O’Hagan
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland Insight Centre for Data Analytics, University College Dublin, Dublin 4, Ireland
*
*Corresponding author. E-mail: [email protected]
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Abstract

The mvClaim package in R provides flexible modelling frameworks for multivariate insurance claim severity modelling. The current version of the package implements a parsimonious mixture of experts (MoE) model family with bivariate gamma distributions, as introduced in Hu et al., and a finite mixture of copula regressions within the MoE framework as in Hu & O’Hagan. This paper presents the modelling approach theory briefly and the usage of the models in the package in detail. This package is hosted on GitHub at https://github.com/senhu/.

Keywords

A priori ratemakingBivariate gamma distributionCopulaGeneral insuranceGeneralised linear modelModel-based clusteringMixture of experts modelMixture of copulas
Type
Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 2 , July 2021 , pp. 441 - 457
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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References

Arakelian, V. & Karlis, D. (2014). Clustering dependencies via mixtures of copulas. Communications in Statistics - Simulation and Computation, 43(7), 1644–1661.CrossRefGoogle Scholar
Benaglia, T., Chauveau, D., Hunter, D.R. & Young, D. (2009). mixtools: An R package for analyzing finite mixture models. Journal of Statistical Software, 32(6), 1–29.CrossRefGoogle Scholar
Bermúdez, L. & Karlis, D. (2012). A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking. Computational Statistics & Data Analysis, 56(12), 3988–3999.CrossRefGoogle Scholar
Cheriyan, K. (1941). A bivariate correlated gamma-type distribution function. Journal of the Indian Mathematical Society, 5, 133–144.Google Scholar
Dempster, A.P., Laird, N.M. & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39, 1–38.CrossRefGoogle Scholar
Grün, B. & Leisch, F. (2007). Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247–5252.CrossRefGoogle Scholar
Grün, B. & Leisch, F. (2008). FlexMix version 2: Finite mixtures with concomitant variables and varying and constant parameters. Journal of Statistical Software, 28(4), 1–35.CrossRefGoogle Scholar
Hofert, M., Kojadinovic, I., Maechler, M. & Yan, J. (2018). copula: Multivariate Dependence with Copulas. R package version 0.999-19.1.Google Scholar
Hu, S., Murphy, T.B. & O’Hagan, A. (2019). Bivariate gamma mixture of experts models for joint insurance claims modelling. To appear; arXiv: arxiv.org/abs/1904.04699.Google Scholar
Hu, S. & O’Hagan, A. (2021). Copula averaging for tail dependence in insurance claims data. To appear; arxiv.org/abs/2103.10912Google Scholar
Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall/CRC, Boca Raton.Google Scholar
Joe, H. (2014). Dependence Modeling with Copulas. Chapman & Hall/CRC, Boca Raton.CrossRefGoogle Scholar
Kosmidis, I. & Karlis, D. (2016). Model-based clustering using copulas with applications. Statistics and Computing, 26(5), 1079–1099.CrossRefGoogle Scholar
Kraemer, N., Brechmann, E., Silvestrini, D. & Czado, C. (2013). Total loss estimation using copula-based regression models. Insurance: Mathematics and Economics, 53, 829–839.Google Scholar
Masarotto, G. & Varin, C. (2017). Gaussian copula regression in R. Journal of Statistical Software, 77(8), 1–26.CrossRefGoogle Scholar
Mathai, A.M. & Moschopoulos, P.G. (1991). On a multivariate gamma. Journal of Multivariate Analysis, 39(1), 135–153.CrossRefGoogle Scholar
Murphy, K. & Murphy, T.B. (2019). MoEClust: Gaussian Parsimonious Clustering Models with Covariates and a Noise Component. R package version 1.2.2.Google Scholar
Murphy, K. & Murphy, T.B. (2020). Gaussian parsimonious clustering models with covariates and a noise component. Advances in Data Analysis and Classification. 14(2), 293–325CrossRefGoogle Scholar
Nelder, J.A. & Wedderburn, R.W.M. (1972). Generalized linear models. Journal of the Royal Statistical Society. Series A (General), 135(3), 370–384.CrossRefGoogle Scholar
Nelsen, R.B. (2007). An Introduction to Copulas. Springer, New York.Google Scholar
R Core Team (2019). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
Ramabhadran, V. (1951). A multivariate Gamma-type distribution. Sankhya, 11, 45–46.Google Scholar
Scrucca, L., Fop, M., Murphy, T.B. & Raftery, A.E. (2016). mclust 5: clustering, classification and density estimation using Gaussian finite mixture models. The R Journal. 8(1), 205–233.CrossRefGoogle ScholarPubMed
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut Statistique de l’Université de Paris, 8, 229–231.Google Scholar
Wang, K., Ng, A. & McLachlan, G. (2018). EMMIXskew: The EM Algorithm and Skew Mixture Distribution. R package version 1.0.3.Google Scholar
Yan, J. (2007). Enjoy the joy of copulas: with a package copula. Journal of Statistical Software, 21(4), 1–21.CrossRefGoogle Scholar