IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i16p2440-d1450880.html
   My bibliography  Save this article

A Review of Wrapped Distributions for Circular Data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/16/2440/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/16/2440/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fernández de Marcos Giménez de los Galanes, Alberto, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    4. Andrew Harvey & Dario Palumbo, 2023. "Regime switching models for circular and linear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 374-392, July.
    5. Harvey, Andrew & Hurn, Stan & Palumbo, Dario & Thiele, Stephen, 2024. "Modelling circular time series," Journal of Econometrics, Elsevier, vol. 239(1).
    6. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    7. Ahmad M. H. Al-khazaleh & Shawkat Alkhazaleh, 2019. "On Wrapping of Quasi Lindley Distribution," Mathematics, MDPI, vol. 7(10), pages 1-9, October.
    8. Xu Qin & Huiqun Gao, 2024. "Nonparametric binary regression models with spherical predictors based on the random forests kernel," Computational Statistics, Springer, vol. 39(6), pages 3031-3048, September.
    9. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    10. Kanti V. Mardia & Karthik Sriram, 2023. "Families of Discrete Circular Distributions with Some Novel Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-42, February.
    11. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    12. Sungsu Kim & Ashis SenGupta, 2013. "A three-parameter generalized von Mises distribution," Statistical Papers, Springer, vol. 54(3), pages 685-693, August.
    13. M. Jones & Arthur Pewsey & Shogo Kato, 2015. "On a class of circulas: copulas for circular distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 843-862, October.
    14. 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.
    15. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    16. Kim, Sungsu & SenGupta, Ashis & Arnold, Barry C., 2016. "A multivariate circular distribution with applications to the protein structure prediction problem," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 374-382.
    17. Carnicero, José Antonio, 2008. "A semi-parametric model for circular data based on mixtures of beta distributions," DES - Working Papers. Statistics and Econometrics. WS ws081305, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. José T.A.S. Ferreira & Miguel A Juárez & MArk F.J. Steel, 2005. "Directional Log-spline Distributions," Econometrics 0511001, University Library of Munich, Germany.
    19. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.
    20. Célestin C. Kokonendji & Aboubacar Y. Touré & Rahma Abid, 2022. "On General Exponential Weight Functions and Variation Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 924-940, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2440-:d:1450880. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.