Applications of Poisson Distribution and Negative Binomial Distribution in Stochastic Simulation of Number of Claims

This paper discusses the properties and relationship between the negative binomial distribution and Poisson distribution in order to use them in the stochastic simulation of number of claims.Finally,it analyzes an example by using Sas software.Negative binomial distribution is a gamma mixture of Poisson distribution.When claim frequency in tensities has positive contagion,the claim number distribution is negative binomial distribution.Since the variance is bigger than the mean,it is a better description of the non-homogeneous risk.