E-statistics (energy statistics)
Research and software related to E-statistics
Gabor J. Szekely, National Science Foundation
Maria L. Rizzo,
Bowling Green State University, email:
Software for R:
This software is distributed under
Public License Version 2, or later. See
COPYING for the license.
R: Energy statistics are implemented in the contributed
energy for R.
R is a free software environment
for statistical computing and graphics, available at
[go to References]
[go to recent changes in energy package]
[go to energy for MATLAB]
Questions or comments on software: Maria Rizzo, email address above
Current version energy_1.2-0 released 27-Sept-2010.
Description of energy package
Title: E-statistics (energy statistics)
Author: Maria L. Rizzo and Gabor J. Szekely
Description: energy: E-statistics (energy statistics)
E-statistics (energy) tests and statistics for comparing distributions:
multivariate normality, multivariate distance components and
k-sample test for equal distributions, hierarchical clustering by e-distances,
multivariate independence tests, distance correlation, goodness-of-fit tests.
Energy-statistics concept based on a generalization of Newton's potential
energy is due to Gabor J. Szekely.
- Maria L. Rizzo and Gabor J. Szekely (2010).
DISCO Analysis: A Nonparametric Extension of Analysis of Variance,
Annals of Applied Statistics Vol. 4, No. 2, 1034-1055.
- Gabor J. Szekely and Maria L. Rizzo (2009). Brownian Distance
Annals of Applied Statistics,
Vol. 3, No. 4, 1236-1265.
- Gabor J. Szekely and Maria L. Rizzo (2009). Rejoinder: Brownian Distance.
Covariance, Annals of Applied Statistics, Vol. 3, No. 4, 1303-1308.
- Maria. L. Rizzo (2009). New Goodness-of-Fit Tests for Pareto Distributions,
ASTIN Bulletin: Journal of the International Association of Actuaries,
- G. J. Szekely, M. L. Rizzo, and N. K. Bakirov (2007).
Measuring and Testing Independence by Correlation of Distances, Annals of Statistics,
Vol. 35 No. 6, pp. 2769-2794.
Bakirov, N. K., Rizzo, M. L., and Szekely, G. J. (2006).
A Multivariate Nonparametric Test of Independence, Journal of Multivariate Analysis
Volume 97, Issue 8 , September 2006, Pages 1742-1756
- Szekely, G. J. and Rizzo, M. L. (2005) Hierarchical Clustering
via Joint Between-Within Distances: Extending Ward's Minimum Variance Method,
Journal of Classification, 22(2) 151-183.
- Szekely, G. J. and Rizzo, M. L. (2005) A New Test for
Journal of Multivariate Analysis,
- Szekely, G. J. and Rizzo, M. L. (2004b) Mean Distance Test of Poisson Distribution,
Statistics and Probability Letters, 67/3, 241-247
- Rizzo, M. L. (2003) Hierarchical Clustering Based on a Generalized
Measure of Homogeneity,
2003 Proceedings of the Joint Statistical Meetings, American Statistical
Association, Section for Physical and Engineering Sciences [CD-ROM],
Alexandria, VA: American Statistical Association.
- Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal
Distributions in High Dimension, InterStat, Nov. (5).
- M. L. Rizzo (2005) Minimum Energy Clustering
Proceedings of Interface/Classification Society of North America,
Joint Annual Meeting, 2005.
- Rizzo, M. L. (2002a). A Test of Homogeneity for Two Multivariate Populations,
2002 Proceedings of the American Statistical Association, Physical and Engineering
Sciences Section [CD-ROM], Alexandria, VA: American Statistical Association.
- Rizzo, M. L. (2002b). A New Rotation Invariant Goodness-of-Fit Test,
Ph.D. dissertation, Bowling Green State University.
- Szekely, G. J. (2000) E-statistics: Energy of
Statistical Samples, Bowling Green State University, Department of
Mathematics and Statistics Technical Report No. 03-05.
- Szekely, G. J. (1989) Potential and Kinetic Energy in Statistics,
Lecture Notes, Budapest Institute of Technology (Technical University).
disco (DIStance COmponents) function and test added in
energy (version 1.2-0 27-Sept-2010) disco provides a nonparametric approach to analysis
of structured data, using distance components rather than variance components.
The statistic is related to, but not equivalent to, the ksample statistic.
A disco method has been added to the eqdist.etest function and the corresponding
The dcov package is now merged into energy version 1.1-0
package, available on CRAN 07-Apr-2008. Please update energy and uninstall dcov.
Some functions in energy have been translated to Matlab.
Minimum energy clustering implemented for Matlab:
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