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Probabilistic model for two dependent circular variables

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  • Harshinder Singh

Abstract

Motivated by problems in molecular biology and molecular physics, we propose a five-parameter torus analogue of the bivariate normal distribution for modelling the distribution of two circular random variables. The conditional distributions of the proposed distribution are von Mises. The marginal distributions are symmetric around their means and are either unimodal or bimodal. The type of shape depends on the configuration of parameters, and we derive the conditions that ensure a specific shape. The utility of the proposed distribution is illustrated by the modelling of angular variables in a short linear peptide. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Harshinder Singh, 2002. "Probabilistic model for two dependent circular variables," Biometrika, Biometrika Trust, vol. 89(3), pages 719-723, August.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:3:p:719-723
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    Citations

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    Cited by:

    1. Aerambamoorthy Thavaneswaran & Nalini Ravishanker, 2023. "Estimating Functions for Circular Time Series Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 198-213, February.
    2. 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.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    4. Kanti Mardia, 2010. "Bayesian analysis for bivariate von Mises distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 515-528.
    5. Fernández-Durán Juan José & Gregorio-Domínguez MarÍa Mercedes, 2014. "Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 1-18, February.
    6. Mark Irwin & Noel Cressie & Gardar Johannesson, 2002. "Spatial-temporal nonlinear filtering based on hierarchical statistical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 249-302, December.
    7. Simon Byrne & Mark Girolami, 2013. "Geodesic Monte Carlo on Embedded Manifolds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 825-845, December.
    8. Marco Marzio & Stefania Fensore & Agnese Panzera & Charles C. Taylor, 2018. "Circular local likelihood," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 921-945, December.
    9. Loic Matthey & Paul M Bays & Peter Dayan, 2015. "A Probabilistic Palimpsest Model of Visual Short-term Memory," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-34, January.
    10. Mohammad Arashi & Najmeh Nakhaei Rad & Andriette Bekker & Wolf-Dieter Schubert, 2021. "Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    11. Saptarshi Chakraborty & Samuel W. K. Wong, 2023. "On the circular correlation coefficients for bivariate von Mises distributions on a torus," Statistical Papers, Springer, vol. 64(2), pages 643-675, April.
    12. David B. Dahl & Ryan Day & Jerry W. Tsai, 2017. "Random Partition Distribution Indexed by Pairwise Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 721-732, April.

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