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A General Approach for Obtaining Wrapped Circular Distributions via Mixtures

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  • S. Rao Jammalamadaka

    (University of California)

  • Tomasz J. Kozubowski

    (University of Nevada)

Abstract

We show that the operations of mixing and wrapping linear distributions around a unit circle commute, and can produce a wide variety of circular models. In particular, we show that many wrapped circular models studied in the literature can be obtained as scale mixtures of just the wrapped Gaussian and the wrapped exponential distributions, and inherit many properties from these two basic models. We also point out how this general approach can produce flexible asymmetric circular models, the need for which has been noted by many authors.

Suggested Citation

  • S. Rao Jammalamadaka & Tomasz J. Kozubowski, 2017. "A General Approach for Obtaining Wrapped Circular Distributions via Mixtures," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 133-157, February.
    • Handle: RePEc:spr:sankha:v:79:y:2017:i:1:d:10.1007_s13171-017-0096-4
    DOI: 10.1007/s13171-017-0096-4
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    References listed on IDEAS

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    1. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    2. William Reed & Arthur Pewsey, 2009. "Two nested families of skew-symmetric circular distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 516-528, November.
    3. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    4. Stefanski, Leonard A., 1991. "A normal scale mixture representation of the logistic distribution," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 69-70, January.
    5. Pewsey, Arthur, 2008. "The wrapped stable family of distributions as a flexible model for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1516-1523, January.
    6. Kim, Hyoung-Moon & Genton, Marc G., 2011. "Characteristic functions of scale mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1105-1117, August.
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    Cited by:

    1. Joseph D. Bailey & Edward A. Codling, 2021. "Emergence of the wrapped Cauchy distribution in mixed directional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 229-246, June.
    2. Stergios B. Fotopoulos & Alex Paparas & Venkata K. Jandhyala, 2020. "Multivariate generalized hyperbolic laws for modeling financial log‐returns: Empirical and theoretical considerations," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 757-775, September.

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