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.
Find related papers by JEL classification: C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics C5 - Mathematical and Quantitative Methods - - Econometric Modeling C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
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