Abstract The aim of this paper is to highlight the use of Zero inflated Poisson distribution and Hurdle Poisson distribution to improve goodness of fit of data with excess zeros. Claim frequency data were used for the Singapore motor insurance database available on the internet. The data are tested for the detection of excess zeros. Parameters of Zero inflated Poisson distribution are estimated using method of moments and method of maximum likelihood. Mean and variance formulas are derived for the distribution of Hurdle Poisson and estimators of method of moment and maximum likelihood of unknown parameters are derived. Parameters of Hurdle Poisson are estimated. The data are modeled using Poisson distribution, Zero inflated Poisson distribution and Hurdle Poisson distribution. Goodness of fit are tested using Chi Square test. The best distribution in the study is selected using AIC & BIC criteria. Hurdle Poisson is the best distribution for modeling the data.