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Discretization is a common decision analysis technique for which many methods are described in the literature and employed in practice. The accuracy of these methods is typically judged by how well they match the mean, variance, and possibly higher moments of the underlying continuous probability distribution. Previous authors have analyzed the accuracy of differing discretization methods across a limited set of distributions drawn from particular families e.g., the bell-shaped beta distributions. In this paper, we extend this area of research by i using the Pearson distribution system to consider a wide range of distribution shapes and ii including common, but previously unexplored, discretization methods. In addition, we propose new three-point discretizations tailored to specific distribution types that improve upon existing methods.