Assessing the Performance of the Discrete Generalised Pareto Distribution in Modelling Non-Life Insurance Claims

Abstract: In this paper, non-life insurance claims were modelled under the three parameter discrete generalised Pareto distribution. Data from the National Insurance Commission of Ghana on reported and settled claims were considered for the period 2012-2016. The maximum likelihood estimation principle was adopted in fitting the discrete Pareto distribution to the yearly and aggregated data. The estimation involved two steps. Firstly, the $\mu$ and $(\mu+1)$ frequency method of \citet{Prieto2014} was modified to suit the characteristics of the data under study. Secondly, a bootstrap algorithm was implemented to obtain the standard errors of the estimators of the parameters of the discrete generalised Pareto distribution. The performance of the discrete generalised Pareto distribution is compared to the negative binomial distribution in modelling the non-life insurance claims data using the information criteria of Akaike and Bayesian. The results show that the discrete generalised Pareto distribution provides a better fit to the non-life claims data. Keywords: Non-life insurance claims, discrete generalised Pareto distribution, negative binomial distribution, maximum likelihood estimation, information criteria.