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A Review of Wrapped Distributions for Circular Data

Author

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  • William Bell

    (Department of Mathematics, University of Manchester, Manchester M13 9PL, UK)

  • Saralees Nadarajah

    (Department of Mathematics, University of Manchester, Manchester M13 9PL, UK)

Abstract

The wrapped method is the most widely used method for constructing distributions for circular data. In this paper, we provide a review of all known wrapped distributions, including 45 distributions for continuous circular data and 10 distributions for discrete circular data. For each wrapped distribution, we state its n th trigonometric moment, mean direction, mean resultant length, skewness, and kurtosis. We also discuss data applications and limitations of each wrapped distribution. This review could be a useful reference and encourage the development of more wrapped distributions. We also mention an R package available for fitting all of the reviewed distributions and illustrate its applications.

Suggested Citation

  • William Bell & Saralees Nadarajah, 2024. "A Review of Wrapped Distributions for Circular Data," Mathematics, MDPI, vol. 12(16), pages 1-51, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2440-:d:1450880
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    References listed on IDEAS

    as
    1. 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.
    2. Roy, Shongkour & Adnan, Mian Arif Shams, 2012. "Wrapped weighted exponential distributions," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 77-83.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder on: 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 76-82, March.
    4. J. J. Fernández-Durán, 2004. "Circular Distributions Based on Nonnegative Trigonometric Sums," Biometrics, The International Biometric Society, vol. 60(2), pages 499-503, June.
    5. Savitri Joshi & K. K. Jose, 2018. "Wrapped Lindley distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1013-1021, March.
    6. 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.
    7. 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.
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