Since observed velocity distributions of particles in the magnetosphere generally have a suprathermal tail instead of an exponential one, we propose to recalculate the density and temperature distributions in a nonrotating ion exosphere with a Lorentzian velocity distribution function (VDF) instead of a Maxwellian. The number density, the flux of particles, parallel and perpendicular pressures, and energy flux of the different classes of particles in the exosphere have been determined for any value of the index &kgr; characterizing the Lorentzian VDF. The barometric density and temperature distributions for a Maxwellian VDF and for a Lorentzian VDF are compared. It is shown that for particles in an attractive potential, the barometric density decreases more slowly with altitude for the Lorentzian VDF. Furthermore, the temperature increases with altitude in this case, while for a Maxwellian VDF, it is independent of altitude. It is suggested that positive gradients of the ion and electron temperatures observed between the topside ionosphere and the outer plasmasphere can be explained by this effect, that is, a non-Maxwellian VDF with an enhanced suprathermal tail. ¿ American Geophysical Union 1996