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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
Authors
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
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Abstract
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.
Keywords
EM Algorithm, Maximum Likelihood, Finite Mixture, Comprehensive Insurance Policy, AIC
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. doi: 10.11648/j.ijsd.20170304.19
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