Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-26T05:45:18.293Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  05 April 2021

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: sen.hu.1@ucdconnect.ie

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/.

Type
Paper
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arakelian, V. & Karlis, D. (2014). Clustering dependencies via mixtures of copulas. Communications in Statistics - Simulation and Computation, 43(7), 16441661.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), 129.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), 39883999.CrossRefGoogle Scholar
Cheriyan, K. (1941). A bivariate correlated gamma-type distribution function. Journal of the Indian Mathematical Society, 5, 133144.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, 138.CrossRefGoogle Scholar
Grün, B. & Leisch, F. (2007). Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 52475252.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), 135.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), 10791099.CrossRefGoogle Scholar
Kraemer, N., Brechmann, E., Silvestrini, D. & Czado, C. (2013). Total loss estimation using copula-based regression models. Insurance: Mathematics and Economics, 53, 829839.Google Scholar
Masarotto, G. & Varin, C. (2017). Gaussian copula regression in R. Journal of Statistical Software, 77(8), 126.CrossRefGoogle Scholar
Mathai, A.M. & Moschopoulos, P.G. (1991). On a multivariate gamma. Journal of Multivariate Analysis, 39(1), 135153.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), 293325CrossRefGoogle Scholar
Nelder, J.A. & Wedderburn, R.W.M. (1972). Generalized linear models. Journal of the Royal Statistical Society. Series A (General), 135(3), 370384.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, 4546.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), 205233.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, 229231.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), 121.CrossRefGoogle Scholar