Publication: A semi-parametric model for circular data based on mixtures of beta distributions
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2008-03
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Abstract
This paper introduces a new, semi-parametric model for circular data, based on mixtures of
shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial
density model which is well known to provide good approximations to any density with finite
support and it is shown that, as for the Bernstein polynomial model, the trigonometric moments of
the SSB mixture model can all be derived.
Two methods of fitting the SSB mixture model are considered. Firstly, a classical, maximum
likelihood approach for fitting mixtures of a given number of SSB components is introduced. The
Bayesian information criterion is then used for model selection. Secondly, a Bayesian approach
using Gibbs sampling is considered. In this case, the number of mixture components is selected
via an appropriate deviance information criterion.
Both approaches are illustrated with real data sets and the results are compared with those
obtained using Bernstein polynomials and mixtures of von Mises distributions.
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Circular data, Shifted, scaled, beta distribution, Mixture models, Bernstein polynomials