Abstract:
,e generalised Pareto distribution (GPD) offers a family of probability spaces which support threshold exceedances and is thus
suitable for modelling high-end actuarial risks. Nonetheless, its distributional continuity presents a critical limitation in characterising
data of discrete forms. Discretising the GPD, therefore, yields a derived distribution which accommodates the count data while
maintaining the essential tail modelling properties of the GPD. In this paper, we model non-life insurance claims under the threeparameter discrete generalised Pareto (DGP) distribution. Data for the study on reported and settled claims, spanning the period
2012–2016, were obtained from the National Insurance Commission, Ghana. ,e maximum likelihood estimation (MLE) principle
was adopted in fitting the DGP to yearly and aggregated data.,e estimation involved two steps. First, we propose a modification to the
μ and (μ + 1) frequency method in the literature. ,e proposal provides an alternative routine for generating initial estimators for
MLE, in cases of varied count intervals, as is a characteristic of the claim data under study. Second, a bootstrap algorithm is
implemented to obtain standard errors of estimators of the DGP parameters. ,e performance of the DGP is compared to the negative
binomial distribution in modelling the claim data using the Akaike and Bayesian information criteria.,e results show that the DGP is
appropriate for modelling the count of non-life insurance claims and provides a better fit to the regulatory claim data considered
