Non-orthogonal multiple access (NOMA) is a compelling strategy that helps wireless networks of the fifth-generation (5G) to fulfill the diverse demands of increased fairness, high reliability, extensive connectivity, low delay and superior performance. Traditionally, NOMA network presumes perfect transmitter-side channel state information (CSI), which is almost impossible for a number of communication scenarios. Furthermore, this paper contemplates the realistic NOMA downlink method in the Rayleigh fading networks, where the statistical CSI linked with each user is known to the transmitter. We evaluate the outage probability of the proposed model and obtain a closed-form framework of the probability of outage for each user. Besides, the source can optimize the network’s achievable sum-rate for different users based on statistical CSI. The precision of our outage probability analysis and the optimum power allocation algorithm proposed are both verified by the analytical and simulation results.