In this work, we present a non linear non Gaussian and incremental Statistical Timing Analysis (SSTA) framework. Specifically, unlike current approaches for non linear non Gaussian SSTA which have numerical components, our approach is a completely analytical. We also investigate the incremental aspects of SSTA and present (1) a fast yet accurate incremental approach (2) a method to efficiently estimate the expected error injected by the incremental SSTA, which could be used to decide, when accurate SSTA should be executed and when incremental SSTA would suffice. Our approach (non incremental) is about 9588 times faster than Monte Carlo whereas an existing state of the art non linear non Gaussian SSTA engine is only 31.3 times faster. Both had comparable errors w.r.t. Monte Carlo. Our incremental approach is 23 times faster than the accurate SSTA approach. Moreover, our error estimating methodology can accurately capture the trends of error injection due to incremental SSTA. Therefore, it could be used to predict when accurate SSTA is needed and when incremental is sufficient.