The statistical distribution of a sum of Ricean random variables occurs extensively in wireless communications. A closed-form expression does not exist for the sum distribution and, furthermore, the Ricean random variable does not have a closed-form characteristic function. For these reasons, it is somewhat difficult to numerically calculate the sum distribution. Highly accurate, closed-form approximations for the sum distributions and densities are presented. These approximations are valid for a wide range of argument values, Rice factors and number of summands.