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Moore Rayleigh test

The Moore-Rayleigh test is a nonparametric test for spherical symmetry. In two dimensions it is known as the Moore test. Its generalization to three or more dimensions has been introduced in the technical report MI-2009-05. In three dimensions, the Moore-Rayleigh test statistic can be efficiently evaluated (with high precision) from a combinatorial sum representation. This allows to run a large number of tests in a short time, as needed, e.g., in neuroscientific applications.

  • Download R package: MooreRayleigh_1.1-2.tar.gz (beta-release 2010-05-09)
  • Download Technical Report
  • View ChangeLog
  • Todo: make C++ version available

Dissimilarity analysis of time series by Wasserstein distances

Wasserstein distances are a class of distances between probability measures. In the discrete case, the latter correspond to (weighted) point sets. Alternatively, time series can be considered such a point set, and the Wasserstein distance quantifies the “distance” between two such series. Delay embedding of time series results in multi-dimensional point sets, and also for these the Wasserstein distances provide meaningful distance measures.

  • Software provided:
    • wassersteinCC: a command-line utility that calculates Wasserstein distances for two ASCII input files. Included is also a (rudimentary) Matlab interface
    • dts: a comprehensive collection of routines for the statistical software environment R. Provides facilities to calculate Wasserstein distances and to analyse the resulting distance matrices (LDA/CCA classification, permutation tests, cross-validation of MDS representations). Additionally, facilities for (multi-exponent) detrended fluctuation analysis (DFA) is provided, as well as routines for fitting power-law and log-normal distributions. (…coming soon…)
  • Download wassersteinCC_0.1.tar.gz (beta-release 2010-09-09)
  • Download dts.tar.gz (…coming soon…)
  • References:
    • Muskulus M, Verduyn-Lunel S: Wasserstein distances in the analysis of time series and dynamical systems. Physica D 240 (2011), 45-58. doi:10.1016/j.physd.2010.08.005
    • Muskulus M, Houweling S, Verduyn-Lunel S, Daffertshofer A. Functional similarities and distance properties. Journal of Neuroscience Methods 183 (2009), 31-41. doi:10.1016/j.jneumeth.2009.06.035
    • Muskulus M, Slats A, Sterk PJ, Verduyn-Lunel S. Fluctuations and determinism of respiratory impedance in asthma and chronic obstructive pulmonary disease. Journal of Applied Physiology (to appear). doi:10.1152/japplphysiol.01414.2009 [application of these codes]
  • Todo
    • Improve scaling (from real distances to integer costs)
    • Improve Matlab interface


All software listed in this section is free software, unless otherwise stated, licensed under the GPL which gives you the rights to freely use, copy and modify the software under certain conditions. Licenses for commercial or other use can be obtained separately.

Academic users, although you are not required by the license to do so, please give credit and cite the given paper or technical report if you use the software in your own research. I would also appreciate very much, if you send me a preprint/reprint (preferred electronically) of publications using or making reference to the software.