




Estatistics (energy statistics)
Research and software related to Estatistics
Gabor J. Szekely, National Science Foundation
Maria L. Rizzo,
Bowling Green State University, email:
Software for R:
energy
This software is distributed under
GNU General
Public License Version 2, or later. See
COPYING for the license.
R: Energy statistics are implemented in the contributed
package
energy for R.
R is a free software environment
for statistical computing and graphics, available at
CRAN.
[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_1.20 released 27Sept2010.
Description of energy package
Package: energy
Title: Estatistics (energy statistics)
Version: 1.20
Date: 20100927
Author: Maria L. Rizzo and Gabor J. Szekely
Description: energy: Estatistics (energy statistics)
Estatistics (energy) tests and statistics for comparing distributions:
multivariate normality, multivariate distance components and
ksample test for equal distributions, hierarchical clustering by edistances,
multivariate independence tests, distance correlation, goodnessoffit tests.
Energystatistics concept based on a generalization of Newton's potential
energy is due to Gabor J. Szekely.
References
 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, 10341055.
Reprint
DOI
 Gabor J. Szekely and Maria L. Rizzo (2009). Brownian Distance
Covariance,
Annals of Applied Statistics,
Vol. 3, No. 4, 12361265.
Reprint
doi:10.1214/09AOAS312
 Gabor J. Szekely and Maria L. Rizzo (2009). Rejoinder: Brownian Distance.
Covariance, Annals of Applied Statistics, Vol. 3, No. 4, 13031308.
Reprint
doi:10.1214/09AOAS312REJ
 Maria. L. Rizzo (2009). New GoodnessofFit Tests for Pareto Distributions,
ASTIN Bulletin: Journal of the International Association of Actuaries,
39/2, 691715.
 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. 27692794.
http://dx.doi.org/10.1214/009053607000000505.
Reprint

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 17421756
http://dx.doi.org/10.1016/j.jmva.2005.10.005.
 Szekely, G. J. and Rizzo, M. L. (2005) Hierarchical Clustering
via Joint BetweenWithin Distances: Extending Ward's Minimum Variance Method,
Journal of Classification, 22(2) 151183.
http://dx.doi.org/10.1007/s0035700500129.
 Szekely, G. J. and Rizzo, M. L. (2005) A New Test for
Multivariate Normality,
Journal of Multivariate Analysis,
93/1, 5880.
http://dx.doi.org/10.1016/j.jmva.2003.12.002.
 Szekely, G. J. and Rizzo, M. L. (2004b) Mean Distance Test of Poisson Distribution,
Statistics and Probability Letters, 67/3, 241247
http://dx.doi.org/10.1016/j.spl.2004.01.005.
 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 [CDROM],
Alexandria, VA: American Statistical Association.
 Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal
Distributions in High Dimension, InterStat, Nov. (5).
Reprint
 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 [CDROM], Alexandria, VA: American Statistical Association.
 Rizzo, M. L. (2002b). A New Rotation Invariant GoodnessofFit Test,
Ph.D. dissertation, Bowling Green State University.
Abstract
 Szekely, G. J. (2000) Estatistics: Energy of
Statistical Samples, Bowling Green State University, Department of
Mathematics and Statistics Technical Report No. 0305.
 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 1.20 27Sept2010) 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
eqdist.e statistic.
Distance Correlation
The dcov package is now merged into energy version 1.10
package, available on CRAN 07Apr2008. Please update energy and uninstall dcov.
Some functions in energy have been translated to Matlab.
Minimum energy clustering implemented for Matlab:
elinkage.m,
Example 1,
Example 2.
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