The distribution function of electrons accelerated by intense laser pulses at steep vacuumplasma 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 highenergy 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. a)