An Entropy-Based Goodness of Fit Statistic for the von Mises Distribution

by Ulric J. Lund, S.R. Jammalamadaka .

Abstract: The maximum entropy characterization of the von Mises distribution on the circle is exploited to derive a consistent goodness of fit test statistic for the von Mises distribution. Monte Carlo simulation results are tabulated giving critical values of the test statistic for various sample sizes and values of the concentration parameter. A power analysis is presented for various alternative hypotheses, comparing the entropy statistic to two competing goodness of fit statistics. The entropy statistic is shown to compare favorably and may be more attractive, especially considering its ease of computation. Finally, it is cautioned that the maximum entropy statistic, which is derived under the assumption that the mean direction is well-defined, is not appropriate for differentiating between the von Mises and the uniform distribution on the circle.

Key Words: Circular Statistics, Entropy, Goodness of Fit, von Mises Distribution

Authors:
Ulric J. Lund, lund@pstat.ucsb.edu
S.R. Jammalamadaka , jammalam@pstat.ucsb.edu

Editor: Wei-Min Huang, wh02@lehigh.edu

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