DAUD: A data driven algorithm to find discrete approximations of unknown continuous distributions

Abstract

Discrete approximation of continuous probability distributions is applied in solving large-scale intractable stochastic models in engineering, business and economics. While the existing approaches rely on the known continuous distribution; to our knowledge, no practical technique exists that approximates the unknown continuous processes. The need for such a technique is heightened with the rise of increasingly larger volumes of data generated by modern systems, while their underlying processes are not fully known. It is important to know that the quality of these approximations can be improved by refining the discretization, however, this comes at the cost of increased computational burden. We thus propose an algorithm that finds a good approximation with minimal discretization based on the convergence behavior of statistical moments. The algorithm was tested with data sets comprising 500 to 1,000,000 data points. The results show robust behavior of the algorithm, especially for the datasets with more than 10,000 data points and for various distribution shapes.