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Directional Log-spline Distributions

Listed author(s):
  • José T.A.S. Ferreira

    (Edeavour Capital Management)

  • Miguel A Juárez

    (University of Warwick)

  • MArk F.J. Steel

    (University of Warwick)

We introduce a new class of distributions to model directional data, based on hyperspherical log-splines. The class is very flexible and can be used to model data that exhibits features that cannot be accommodated by typical parametric distributions, such as asymmetries and multimodality. The distributions are defined on hyperspheres of any dimension and thus, include the most common circular and spherical cases. Due to the flexibility of hyperspherical log-splines, the distributions can approximate well the distribution of any phenomenon and are as smooth as desired. We propose a Bayesian setup for conducting inference with directional log-spline distributions where we pay particular attention to the prior specification and the matching of the priors of the log-splines model and the model constructed through a mixture of von Mises distributions. We compare both models in the context of three data sets: generated data on the circle, a circular application concerning the movement of turtles and a spherical application on the arrival direction of cosmic rays.

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Paper provided by EconWPA in its series Econometrics with number 0511001.

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Length: 16 pages
Date of creation: 01 Nov 2005
Handle: RePEc:wpa:wuwpem:0511001
Note: Type of Document - pdf; pages: 16
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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, 06.
  2. José T. A. S. Ferreira & Mark F. J. Steel, 2005. "Modelling directional dispersion through hyperspherical log-splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 599-616.
  3. A. Mooney, Jennifer & Helms, Peter J. & Jolliffe, Ian T., 2003. "Fitting mixtures of von Mises distributions: a case study involving sudden infant death syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 505-513, January.
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