[en] We derive asymptotic formulas for some of the statistical distributions for a quantum ideal relativistic gas in (d+1) - dimensions, such as the invariant phase space, the grand canonical density of states and the microcanonical density of cluster states. The exact formula for the invariant phase space was given in our previous paper, but those for the latter two densities of states are presented in this paper. For comparison, we also provide the thermodynamical description. (Author)