A Simple and Effective Discretization of a Continuous Random Variable

A generally applicable discretization method is proposed to approximate a continuous distribution on a real line with a discrete one, supported by a finite set. The method adopts a criterion which is shown to be flexible in approximating higher order features of the underlying continuous distribution while automatically preserving mean and variance. To illustrate the effectiveness of the method, several examples covering a wide-range continuous distributions are analyzed. A computer implementation (using ) of the proposed procedure is provided.