A new statistical model for random unit vectors

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Oualkacha, Karim¹  Rivest, Louis-Paul¹ 

[1] Univ Laval, Dept Math & Stat, Ste Foy, PQ G1K 7P4, Canada

关键词: Axial distribution;    Directional data;    Multivariate statistics;    Spherical symmetry;    Quaternion;    Rotation;   

DOI  :  10.1016/j.jmva.2008.03.004

来源: Elsevier

【 摘 要 】

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 3 x 3 rotation matrices by representing them as quaternions, which are unit vectors in R-4. 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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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