Analytical expressions for the lowest-order distribution functions of a plasma that are valid throughout the plasma are generally not easily obtainable when conditions shift from collision dominance in some regions of the plasma to absence of collisions in other regions. Indeed, the reason for the breakdown of classical approximation methods for distribution functions and the corresponding macroscopic equations in plasma kinetic theory is often the lack of such global lowest-order distribution functions. The main purpose of the present paper is to derive an approximate global distribution function for an outflowing dilute light ion component in a polar-region model of the ionosphere where conditions for the light ions shift from collision dominance in low regions to collisionless conditions high up. For this, a simplified collision integral of a form given by Chandrasekhar will be used. The proposed global solution is given after simpler solutions, as a collisionless solution, an exact collision-dominated solution and a solution corresponding to classical transport theory are derived, for reason of comparison, in the first parts of the paper.