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The theory of concentrated Langevin distributions

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  • Watson, Geoffrey S.

Abstract

The density of the Langevin (or Fisher-Von Mises) distribution is proportional to exp ?[mu]'x, where x and the modal vector [mu] are unit vectors in q. ? (>=0) is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are obtained for statistics appropriate when ?1,...,?m are known but tend to infinity, and are unknown but equal to ? which tends to infinity. The three null hypotheses are H01:[mu] = [mu]0(m=1), H02:[mu]1= ... =[mu]m, H03:[mu]i [epsilon] V, I=1,...,m In each case a sequence of alternatives is taken tending to the null hypothesis.

Suggested Citation

  • Watson, Geoffrey S., 1984. "The theory of concentrated Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 74-82, February.
    • Handle: RePEc:eee:jmvana:v:14:y:1984:i:1:p:74-82
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    Cited by:

    1. Toru Kitagawa & Jeff Rowley, 2022. "von Mises-Fisher distributions and their statistical divergence," Papers 2202.05192, arXiv.org, revised Nov 2022.
    2. Chikuse, Yasuko, 2003. "Concentrated matrix Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 375-394, May.
    3. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.

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