A precise ratemaking system allows insurers to cover expected losses, expenses and make adequate provision for contingencies.Thefirststepinratemakingistomodeltheclaimfrequencydistribution.Traditionally,theclaimcount distribution in general insurance is assumed to follow the Poisson and negative binomial (NB) distributions (Thomas andSamson,1987;Renshaw,1994;HabermanandRenshaw,1996).Undertheusualdeductibleagreementingeneral insurance policies, a claim will not be created unless the loss exceeds the prescribed deductible limit. Furthermore, the no claim discount (NCD) system, which is widely adopted by automobile insurers, leads to excess zero claims because policyholders seldom make a claim if the amount to be claimed is small. Such practice results in excess