The purpose of this paper is to develop a statistical model to evaluate the fairness of resource distribution. Two recently proposed fairness score functions are adopted. The developed fairness score functions allow users to have the same or different priority levels. This functions possess all the necessary properties required to be a quantitative measure for the purpose of fairness evaluation. Monte Carlo simulation is used to find the critical values. When the users have the same priority level, a table of the critical values is given for different sample sizes and different significance levels. When the users have different priority levels, it is difficult to generate a similar table since the users' priority levels vary. In this case, a computer program is needed obtain critical values. While the discussion is originally for computer network resource distribution, the method can be used in other fields such as social resource distribution.