Performance Measurement of Probability Distributions in Modelling Non-Life Insurance Claims

Abstract

In this thesis, we model non-life insurance claims by using the two-parameter Negative Binomial (NB) and three-parameter Discrete Generalised Pareto (DGP) distributions. Data from National Insurance Commission (NIC) on Reported and Settled Claims counts for the period 2012 - 2016 were considered. The maximum likelihood estimation (MLE) was adopted to fit Negative Binomial and Discrete Generalised Pareto to the count data. In the latter case, the estimation involved two steps. First, the _ and (_ + 1) frequency method (Prieto et al., 2014) of generating initial estimators, was modified to suit the characteristics of the count data under study. Second, the parameter estimates were obtained by MLE, using the initial values from the modified _ and (_+1) frequency method. In addition, a bootstrap process was used to obtain the standard errors of the estimators of the DGP parameters. The models were compared using the information criteria, AIC and BIC. Under Reported and Settled Claims categories, each criteria was found to favour the DGP model. Therefore, the DGP model is recommended, as it provides a better fit to the non-life claims data.