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A new method for building a discrete analogue to a continuous random variable based on minimization of a distance between distribution functions

In this work, we propose a novel procedure for deriving a discrete counterpart to a continuous probability distribution. This procedure or, better, this class of procedures, is based on an appropriate distance between cumulative distribution functions. A discrete random distribution, supported on the set of integer values, is obtained by minimizing its distance to the assigned continuous probability distribution. An application is provided with reference to the negative exponential distribution, along with a comparison with an existing discretization technique.