In this letter, we statistically analyze the outage performance of non-orthogonal multiple access (NOMA) with CDF-based scheduling (CS) over Nakagami-m fading channels. Based on our system model assumptions, CS selects the multiple users based on CDF of channel gain, which guarantees fair resource allocation. With this CS algorithm, the closed-form of outage is derived to show the effect of CS. Specifically, we first analyze the selection probability of each user and, via the derived distribution results, statistically investigate the outage performance when two users are selected. In addition, we obtain the diversity order that is affected by both the weights of each user and the m parameter of Nakagami-m fading channel. Our analytical results are thoroughly validated by cross-checking them against the results obtained via the Monte-Carlo simulations. Some selected results show that CS exploits multiuser diversity.