A Monte Carlo simulation is used to study the effects of Kappa H+ distributions in the polar wind. We consider the gravity, the polarization electric field, the divergence of geomagnetic field lines and Coulomb collisions of H+ in a background of O+ ions. The aim is to study the consequences of a velocity distribution function with an enhanced high energy tail instead of a Maxwellian distribution as assumed in earlier Monte Carlo simulations. The transformation of the velocity distribution function of H+ ions as a function of the altitude is presented. Effects resulting from the acceleration of the particles by the polarization electric field and from Coulomb collisions depend on the energy of the particles. Coulomb collisions mainly affect low energy particles while high energy particles are more efficiently accelerated by the upward directed ambipolar electric field. The combination of both effects results in double-hump velocity distribution functions developing in the transition region. We study consequences of suprathermal tails distributions on the shape of the double-hump and on the moments of the velocity distribution function.