A method and apparatus of a device that performs a generalized moment based variation aware timing analysis on a circuit design is described. The device receives a signal path that traverses a plurality of gates. For each of the plurality of gates, the device retrieves a statistical distribution that represents delay variation at the gate. The statistical distribution for each gate is measured by a number of statistical moments that include higher order statistical moments besides the mean and the standard deviation of the distribution. The device computes statistical moments to represent the timing variation on the signal path by propagating statistical distributions of the gates on the signal path. The device reconstructs a statistical distribution function for timing variation on the signal path based on the computed statistical moments.