Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims
International Journal of Statistical Distributions and Applications
Volume 3, Issue 4, December 2017, Pages: 124-128
Received: Mar. 1, 2017;
Accepted: May 8, 2017;
Published: Dec. 7, 2017
Views 801 Downloads 44
Nana Kena Frempong, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Osei Tawiah Owusu, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Maxwell Akwasi Boateng, Faculty of Engineering, Ghana Technology University College, Kumasi, Ghana
Francis Kwame Bukari, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Follow on us
The aim of this study is to determine the best mixture model for claim amount from a comprehensive insurance policy portfolio and use the model to estimate the expected claim amount per risk for the coming calendar year. The claims data were obtained from the motor insurance office of one of the top business insurance companies in Ghana. The data consists of one thousand (1,000) claim amounts from January 2012 to December 2014. The expectation-maximization (EM) algorithm within a maximum likelihood framework was used to estimate the parameters of four mixture models namely the Heterogeneous Normal-Normal, Homogeneous Normal-Normal, Pareto-Gamma and Gamma-Gamma. These mixture models were fitted to the claims data and measures of goodness-of-ﬁt (AIC and BIC) were used to determine the best mixture model. The Heterogeneous Normal-Normal mixture distribution was the appropriate model for the motor insurance claims data due to the least AIC. The estimated expected claims amount for the coming calendar year (2015) from the model was GHS 877.672 per risk. This in a way may inform decision makers as to the kind of anticipated reserves for future claims.
EM Algorithm, Maximum Likelihood, Finite Mixture, Comprehensive Insurance Policy, AIC
To cite this article
Nana Kena Frempong,
Osei Tawiah Owusu,
Maxwell Akwasi Boateng,
Francis Kwame Bukari,
Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims, International Journal of Statistical Distributions and Applications.
Vol. 3, No. 4,
2017, pp. 124-128.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Finite Mixture Models. By Geoffrey McLachlan and David Peel. Copyright 2000 John Wiley & Sons, Inc. ISBN: 0-471-00626-2.
Teodorescu, S. (2009). Loss distributions modeling for motor tpl insurance class using Gaussian mixture method and EM algorithm.
Hogg, R. V. and Klugman, S. A. (2008). Modeling Loss Distributions. John Wiley Sons, New York.
Janczuraa, J. and Weron, R. (2010). An empirical comparison of alternate regime-switching models for electricity spot prices. MPRA.
Dempster A, Laird N, Rubin D (1977). “Maximum Likelihood from Incomplete Data via the EM-Alogrithm.” Journal of the Royal Statistical Society, B, 39, 1–38.
Hewitt, C. J. and Leftkowitz, B. (1979). Methods for fitting distributions to insurance loss data. Proc. Casualty Actuarial Science Soc.
Davenport, J., Bezdek, J., and Hathaway, R. (1988). Parameter estimation for finite mixture distributions. Comput. Math. Applica., 15, No. 10: 819–828.
McLachlan, G. and Peel, D. (2008). Finite Mixture Models. John Wiley Sons, Inc., New York.
Atienza, N., Garcia-Heras, J., and Munoz-Pichardo, J. (2006). A new condition for identifiability of finite mixture distributions. Research Gate.
Zhang, L., Gove, J. H., Liu, C., and Leak, W. B. (2001). A finite mixture of two weibull distributions for modeling the diameter distribtuons of rotated-sigmoid, uneven-aged stands. Canadian Journal of Forest Research, 31.
Zhang, H. and Huang, Y. (2015). Finite mixture models and their applications: A review. Austin Biometrics and Biostatistics.
Sattayatham, P. and Talangtam, T. (2012). Fitting of finite mixture distributions to motor insurance claims. Journal of Mathematics and Statistics 8(1): 49-56, ISSN 154-3644.
Gong, Y. R. S. (1999). Gaussian mixture models.
Titterington, D., Smith, A., and Makov, U. (1985). Statistical Analysis of Finite Mixture Distributions. New Yok: Wiley.
Fraley C, Raftery AE (2002b). “Model-Based Clustering, Discriminant Analysis and Density Estimation.” Journal of the American Statistical Association, 97, 611–631.