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Distributions for spherical data based on nonnegative trigonometric sums

Author

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  • J. Fernández-Durán
  • M. Gregorio-Domínguez

Abstract

A family of distributions for a random pair of angles that determine a point on the surface of a three-dimensional unit sphere (three-dimensional directions) is proposed. It is based on the use of nonnegative double trigonometric (Fourier) sums (series). Using this family of distributions, data that possess rotational symmetry, asymmetry or one or more modes can be modeled. In addition, the joint trigonometric moments are expressed in terms of the model parameters. An efficient Newton-like optimization algorithm on manifolds is developed to obtain the maximum likelihood estimates of the parameters. The proposed family is applied to two real data sets studied previously in the literature. The first data set is related to the measurements of magnetic remanence in samples of Precambrian volcanics in Australia and the second to the arrival directions of low mu showers of cosmic rays. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • J. Fernández-Durán & M. Gregorio-Domínguez, 2014. "Distributions for spherical data based on nonnegative trigonometric sums," Statistical Papers, Springer, vol. 55(4), pages 983-1000, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:983-1000
    DOI: 10.1007/s00362-013-0547-5
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    References listed on IDEAS

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    1. J. J. Fernández-Durán, 2004. "Circular Distributions Based on Nonnegative Trigonometric Sums," Biometrics, The International Biometric Society, vol. 60(2), pages 499-503, June.
    2. Hendriks, Harrie, 2003. "Application of fast spherical Fourier transform to density estimation," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 209-221, February.
    3. Adelaide Figueiredo, 2008. "Two-way ANOVA for the Watson distribution defined on the hypersphere," Statistical Papers, Springer, vol. 49(2), pages 363-376, April.
    4. Peel D. & Whiten W. J & McLachlan G. J, 2001. "Fitting Mixtures of Kent Distributions to Aid in Joint Set Identification," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 56-63, March.
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