The random Gaussian surface model proposed by Nayak is important to many statistical summit-based micro contact models. A Gaussian distribution is usually assumed for the summit heights as many surfaces have a Gaussian distribution of surface heights. In this work, based on Nayak’s models the skewness and kurtosis of the summit heights distribution are derived as a function of the bandwidth parameter α. The correctness of these two equations verified using a numerical scheme that generates random Gaussian surfaces with various α values. Also, practical contact simulations are performed to demonstrate the significance of the proposed equations and also to show the error of using a Gaussian distribution versus a correct asymmetric distribution for the summit heights.