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Circular Bernstein polynomial distributions

Author

Listed:
  • Carnicero, José Antonio
  • Wiper, Michael Peter
  • Ausín Olivera, María Concepción

Abstract

This paper introduces a new non-parametric approach to the modeling of circular data, based on the use of Bernstein polynomial densities which generalizes the standard Bernstein polynomial model to account for the specific characteristics of circular data. It is shown that the trigonometric moments of the proposed circular Bernstein polynomial distribution can all be derived in closed form. We comment on how to fit the Bernstein polynomial density approximation to a sample of data and illustrate our approach with a real data example.

Suggested Citation

  • Carnicero, José Antonio & Wiper, Michael Peter & Ausín Olivera, María Concepción, 2010. "Circular Bernstein polynomial distributions," DES - Working Papers. Statistics and Econometrics. WS ws102511, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws102511
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    References listed on IDEAS

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    1. Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393, September.
    2. 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.
    3. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    4. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100, January.
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    Keywords

    Circular data;

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