In this paper, we deal with the performance analysis of a cumulative distribution function (CDF)-based multiuser scheduling scheme for downlink non-orthogonal multiple access (NOMA). With this scheme, the multiple users having relatively better channel gain are selected. We first statistically analyze the probability of user selection in terms of the weight of each user determining the time fraction. We confirm that equal weight ensures fair resource allocation. Under this equal weight condition for fairness, we derive the distribution of signal-to-interference-plus-noise ratio (SINR) when the specific user is selected. Simulation results show that with this scheme, the time resources can be allocated more fairly compared to the proportional fair scheduling scheme, especially under NOMA conditions. Further, by adjusting the weight of desired user, the average rate and selection probability can be controlled.