The site frequency spectrum (SFS) and other genetic summary statistics are at the heart of many population genetic studies. Previous studies have shown that human populations have undergone a recent epoch of fast growth in effective population size. These studies assumed that growth is exponential, and the ensuing models leave an excess amount of extremely rare variants. This suggests that human populations might have experienced a recent growth with speed faster than exponential. Recent studies have introduced a generalized growth model where the growth speed can be faster or slower than exponential. However, only simulation approaches were available for obtaining summary statistics under such generalized models. In this study, we provide expressions to accurately and efficiently evaluate the SFS and other summary statistics under generalized models, which we further implement in a publicly available software. Investigating the power to infer deviation of growth from being exponential, we observed that adequate sample sizes facilitate accurate inference; e.g., a sample of 3000 individuals with the amount of data expected from exome sequencing allows observing and accurately estimating growth with speed deviating by $10% from that of exponential. Applying our inference framework to data from the NHLBI Exome Sequencing Project, we found that a model with a generalized growth epoch fits the observed SFS significantly better than the equivalent model with exponential growth (P-value ¼ 3:85 3 10 26 ). The estimated growth speed significantly deviates from exponential (P-value ( 10 212 ), with the best-fit estimate being of growth speed 12% faster than exponential.KEYWORDS coalescent; generalized models; population growth; human demographic history; software S UMMARY statistics of genetic variation play a vital role in population genetic studies, especially inference of demographic history. In particular, the site frequency spectrum (SFS) is a vital summary statistic of genetic data and is widely utilized by many demographic inference methods applied to humans and other organisms (Marth et al. 2004;Gutenkunst et al. 2009;Excoffier et al. 2013;Bhaskar et al. 2015;Liu and Fu 2015). Some other demographic inference methods are based on the sequential Markov coalescent and utilize the most recent common ancestor (T MRCA ) and linkage disequilibrium patterns (Li and Durbin 2011;Harris and Nielsen 2013;MacLeod et al. 2013;Sheehan et al. 2013;Schiffels and Durbin 2014). As another example, several studies used the average pairwise difference between chromosomes (Hammer et al. 2008;Gottipati et al. 2011;Arbiza et al. 2014) and the SFS (Keinan et al. 2009) to study the relative effective population sizes between the human X chromosome and the autosomes. The wide application of such genetic summary statistics stresses the need for their fast and accurate computation under any model of demographic history, instead of their estimations via simulations or approximations (e.g., Hudson 2002;Gutenkunst et al. 2009).Several ...