The velocity distribution of atomic hydrogen in the earth's exosphere has been calculated as a function of altitude and direction using a Monte Carlo simulation which includes the classical exobase source and the higher-altitude plasmaspheric charge exchange source. The charge exchange 'hot' hydrogen atom source produces the satellite component and 'hot' ballistic and escape components. The velocity distribution functions F(v) have been plotted as log F(v) against v2. For a Maxwellian velocity distribution the slope would be constant with velocity v and inversely proportional to the defined temperature. For the classical exobase source alone the slope is constant only for the upward radial component, and it increases dramatically as the altitude increases above one earth radius for both the incoming radial and the two transverse velocity components. This 'temperature decrease' is the same effect as indicated in the analytical work of Chamberlain (1963), due to the absence of the incoming-hyperbolic and flyby components of the particle distributions. The effect of charge exchange is to enhance the wings of the velocity distributions, especially for the upward-radial component. Charge exchange does not, however, succeed in overcoming the 'temperature decreases' in the incoming-radial and transverse directions at altitudes above one earth radius. The gradients of the 'temperatures' and their anisotropies are great enough to engender some lack of confidence in the results of radiative transfer treatments for Lyman &agr;, which have been carried out so far on the basis of isothermal exospheric hydrogen models.