A mixed Gaussian model for motor insurance claims (Case study: an insurance company in Ghana)

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April, 2016
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The aim of this study was to determine the best mixture model for the claims amount and use the model to determine the expected claim amount per risk for the coming year. The claims data were obtained from the motor insurance department of one of the top three insurance companies in Ghana. The data consists of one thousand and three (1,003) claim amounts from 2012 to 2014. The average claim amount was GHS878.54 with standard deviation GHS339.03. Principles of Maximum likelihood estimation was used to determine the parameters of Heterogeneous Normal-Normal, Homogeneous Normal- Normal and Pareto-Gamma mixture models. The Q-Q plot 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 model that best fit the motor insurance claims data with an expected claims amount of GHS868.40 per risk.
A thesis submitted to The Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirement for the degree of M.Sc Actuarial Science.