The statistical behaviour of intermittent trajectories at the 3/1 resonance is investigated. The elliptic planar restricted three-body problem is used as a model. Distribution functions for time intervals D between eccentricity bursts are obtained and theoretically interpreted. For smaller values of D, the distribution is found to be of Poisson type, while in its tail it is described by a power law D^α. This change in the distribution occurs for values of D in the range 10⁵-10⁶ Jupiter periods. The power-law index α for the integral distributions lies in the range (-2,-1) and is trajectory dependent. The algebraic decay in the tails of the distributions is explained by the phenomenon of sticking of orbits to the chaos border during long intervals between bursts.