A stochastic model of wave groups is presented to explain the occurrence of exceptionally large waves, usually referred to as rogue waves. The model leads to the description of the non-Gaussian statistics of large waves in oceanic turbulence and to a new asymptotic distribution of their crest heights in a form that generalizes the Tayfun model. The new model explains the unusually large crests observed in flume experiments of narrowband waves. However, comparisons with realistic oceanic measurements gathered in the North Sea during an intense storm indicate that the generalized model do not appear to improve upon the original Tayfun distribution.