Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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 June 19, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 16, 2008