**Abstract** : The distribution function of electrons accelerated by intense laser pulses at steep vacuum-plasma interfaces is investigated by using Fokker-Planck equation and methods from extreme statistics. The energy spectrum of electrons penetrating into the dense plasma after being accelerated at the interface and in the pre-plasma shows systematically cutoff-like decrease in the momentum component p x /m e c along the laser propagation axis. While the distribution associated to the kinetic energy spectrum (E kin) is often approximated by a thermal distribution, F(E kin) ∝ exp(−E kin /T h), with a hot particle temperature T h , the nature of the distribution close to the cutoff is clearly non-thermal. Electron distributions are analyzed here from two-dimensional Particle-in-Cell simulations. Via a comparison with solutions derived from a Fokker-Planck equation and based on Chirikov's standard map models, we find that the electron distributions show a clear signature of stochastic heating, due to repeated acceleration in the standing wave in the pre-plasma. Further analysis of the solutions to the Fokker-Planck equation allows us to describe the cutoff seen in the momentum p of the distributions F(p), which can be expressed as a function of time τ in the form F(p, τ) ∝ [(p max − p)/δ p] exp −2p 3 /9τ , portraying a time-dependent cutoff at p → p max. This implies that the energetic tail of the distribution belongs to the maximum domain of attraction of the Weibull law, which means that the probability to find high-energy electrons varies abruptly near p max. The variance of physical observables sensitive to the high-energy tail is consequently considerably higher than when assuming thermal distribution.