A range reduction method for generating discrete random variables

A new general method for generating discrete random variables is presented. The method is based on reducing the problem of generating a discrete random variable with an extremely large range to that of generating a random variable with a small range consisting of a few possible values (i.e. range reduction). The validity of the method presented is proved, and its performance is examined and compared to the performance of previously developed general methods. A random number generator for geometric variables of order r based on the range reduction method is given as an illustration of its advantages.