[en] The relaxation of a collisionless plasma is not regulated by the usual collisional Boltzmann equation and its related H-theorem. The interactions are long range and the collisions are not instantaneous. A direct simulation approach is presented for measuring by computer experiment what the relaxed distribution is. The conclusion of the analysis is that the relaxed distribution includes both a low energy component that is well described using the usual Boltzmann distribution and a high energy tail described using a power law. The results of the simulation study are compared directly with the model recently proposed by Kaniadakis (2002 Phys. Rev. E 66 056125). The observed cumulative distribution function is well reproduced by the theory