The staff in the neonatal intensive care units is required to have highly specialized training and the using equipment in this unit is so expensive. The random number of arrivals, the rejections or transfers due to lack of capacity and the random length of stays, make the advance knowledge of the optimal staff; equipments and materials requirement for levels of the unit behaves as a stochastic process. In this paper, the number of arrivals, the rejections or transfers due to lack of capacity and the random length of stays in a neonatal intensive care unit of a university hospital has been statistically analyzed. The arrival patients are classified according to the levels based on the required nurse: patient ratio and gestation age. Important knowledge such as arrivals, transfers, gender and length of stays are analyzed. Finally, distribution functions for patients' arrivals, rejections and length of stays are obtained for each level in the unit.