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Tractable circula densities from Fourier series

Author

Listed:
  • Shogo Kato

    (Institute of Statistical Mathematics)

  • Arthur Pewsey

    (University of Extremadura)

  • M. C. Jones

    (The Open University)

Abstract

This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.

Suggested Citation

  • Shogo Kato & Arthur Pewsey & M. C. Jones, 2022. "Tractable circula densities from Fourier series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 595-618, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-021-00790-y
    DOI: 10.1007/s11749-021-00790-y
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    References listed on IDEAS

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    1. Jupp, P.E., 2015. "Copulae on products of compact Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 92-98.
    2. Jupp, P.E. & Kume, A., 2020. "Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    3. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    4. Masanobu Taniguchi & Shogo Kato & Hiroaki Ogata & Arthur Pewsey, 2020. "Models for circular data from time series spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 808-829, November.
    5. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    6. Pertsemlidis Alexander & Zelinka Jan & Fondon John W. & Henderson R. Keith & Otwinowski Zbyszek, 2005. "Bayesian Statistical Studies of the Ramachandran Distribution," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-18, November.
    7. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    8. Shogo Kato & M. C. Jones, 2015. "A tractable and interpretable four-parameter family of unimodal distributions on the circle," Biometrika, Biometrika Trust, vol. 102(1), pages 181-190.
    9. Kanti V. Mardia & Charles C. Taylor & Ganesh K. Subramaniam, 2007. "Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data," Biometrics, The International Biometric Society, vol. 63(2), pages 505-512, June.
    10. Grace Shieh & Richard Johnson, 2005. "Inferences based on a bivariate distribution with von Mises marginals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 789-802, December.
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