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A new statistical model for random unit vectors

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  • Oualkacha, Karim
  • Rivest, Louis-Paul

Abstract

This paper proposes a new statistical model for symmetric axial directional data in dimension p. This proposal is an alternative to the Bingham distribution and to the angular central Gaussian family. The statistical properties for this model are presented. An explicit form for its normalizing constant is given and some moments and limiting distributions are derived. The proposed density is shown to apply to the modeling of 3x3 rotation matrices by representing them as quaternions, which are unit vectors in . The moment estimators of the parameters of the new model are calculated; explicit expressions for their sampling variances are given. The analysis of data measuring the posture of the right arm of subjects performing a drilling task illustrates the application of the proposed model.

Suggested Citation

  • Oualkacha, Karim & Rivest, Louis-Paul, 2009. "A new statistical model for random unit vectors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 70-80, January.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:70-80
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    References listed on IDEAS

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    1. D. Rancourt & L.‐P. Rivest & J. Asselin, 2000. "Using orientation statistics to investigate variations in human kinematics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 81-94.
    2. Kim, Peter T., 1991. "Decision theoretic analysis of spherical regression," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 233-240, August.
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    Cited by:

    1. Rau, Christian, 2013. "Bayes classifiers of three-dimensional rotations and the sphere with symmetries," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 930-935.
    2. Melissa A. Bingham & Marissa L. Scray, 2017. "A permutation test for comparing rotational symmetry in three-dimensional rotation data sets," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-8, December.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.

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