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One Dimensional Modeling and Learning



J E. Devaney


This paper introduces four new algorithms, the M-algorithm, the L-algorithm, the S-algorithm and the T-algorithm, which enable recognition of distributional functions without doing a fit of the data to the distribution. These algorithms workbest for large sample sizes, such as $500$ to $50,000$ points. These techniques rest on the concept of an equation signature, which is a coefficient independent property of an equation, and hence enable searching for all instances of an equation type at the same time. The M-algorithm can differentiate even very similar distributions. Additionally it provides accurate values for the distribution location and variation parameters. The L-algorithm can tell if two distributions are the same, even if the distribution type is unknown. Both can also tell if the location and/or variation parameters of the distribution are changing. The S-algorithm can detect whether a distribution is symmetric or not and provide an estimate of its asymmetry. The T-algorithm provides an estimate of the tail length of the distribution. A method to visualize the attributes of a database in terms of distributions, the D-plot, is presented. Applications of these algorithms include detecting redundancy in decision tables and improving machine learning.
NIST Interagency/Internal Report (NISTIR) - 6168
Report Number


constructive induction, D-plot, distribution finding, L-algorithm, learning, M-algorithm, one dimensional modeling, probability plotting, S-algorithm, T-algorithm


Devaney, J. (2008), One Dimensional Modeling and Learning, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD (Accessed December 2, 2023)
Created October 16, 2008