IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v83y2021i2d10.1007_s13571-019-00201-1.html
   My bibliography  Save this article

On Some Circular Distributions Induced by Inverse Stereographic Projection

Author

Listed:
  • Yogendra P. Chaubey

    (Concordia University)

  • Shamal C. Karmaker

    (University of Dhaka)

Abstract

In earlier studies of circular data, the corresponding probability distributions considered were mostly assumed to be symmetric. However, the assumption of symmetry may not be meaningful for some data. Thus there has been increased interest, more recently, in developing skewed circular distributions. In this article we introduce three skewed circular models based on inverse stereographic projection (ISP), originally introduced by Minh and Farnum (Comput. Stat.–Theory Methods, 32, 1–9, 2003), by considering three different versions of skewed-t distribution on real line considered in the literature, namely skewed-t by Azzalini (Scand. J. Stat., 12, 171–178, 1985), two-piece skewed-t, (seemingly first considered in Gibbons and Mylroie Appl. Phys. Lett., 22, 568–569, 1973 and later by Fernández and Steel J. Amer. Statist. Assoc., 93, 359–371 1998) and skewed-t by Jones and Faddy (J. R. Stat. Soc. Ser. B (Stat. Methodol.), 65, 159–174, 2003). Unimodality and skewness of the resulting distributions are addressed in this paper. Further, real data sets are used to illustrate the application of the new models. It is found that under certain condition on the original scaling parameter, the resulting distributions may be unimodal. Furthermore, the study in this paper concludes that ISP circular distributions obtained from skewed distributions on the real line may provide an attractive alternative to other asymmetric unimodal circular distributions, especially when combined with a mixture of uniform circular distribution.

Suggested Citation

  • Yogendra P. Chaubey & Shamal C. Karmaker, 2021. "On Some Circular Distributions Induced by Inverse Stereographic Projection," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 319-341, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-019-00201-1
    DOI: 10.1007/s13571-019-00201-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-019-00201-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13571-019-00201-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. C. Jones & Arthur Pewsey, 2012. "Inverse Batschelet Distributions for Circular Data," Biometrics, The International Biometric Society, vol. 68(1), pages 183-193, March.
    2. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    3. Toshihiro Abe & Arthur Pewsey & Kunio Shimizu, 2013. "Extending circular distributions through transformation of argument," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 833-858, October.
    4. Kato, Shogo & Jones, M. C., 2010. "A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 249-262.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ameijeiras-Alonso, Jose & Gijbels, Irène & Verhasselt, Anneleen, 2022. "On a family of two–piece circular distributions," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

    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. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.
    2. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    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. Christophe Ley & Thomas Verdebout, 2014. "Skew-rotsymmetric Distributions on Unit Spheres and Related Efficient Inferential Proceedures," Working Papers ECARES ECARES 2014-46, ULB -- Universite Libre de Bruxelles.
    5. Mojtaba Hatami & Mohammad Hossein Alamatsaz, 2019. "Skew-symmetric circular distributions and their structural properties," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 953-969, December.
    6. 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.
    7. Jose Ameijeiras-Alonso & Christophe Ley & Arthur Pewsey & Thomas Verdebout, 2021. "On optimal tests for circular reflective symmetry about an unknown central direction," Statistical Papers, Springer, vol. 62(4), pages 1651-1674, August.
    8. Yoichi Miyata & Takayuki Shiohama & Toshihiro Abe, 2023. "Identifiability of Asymmetric Circular and Cylindrical Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1431-1451, August.
    9. Toshihiro Abe & Arthur Pewsey & Kunio Shimizu, 2013. "Extending circular distributions through transformation of argument," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 833-858, October.
    10. M. C. Jones & Arthur Pewsey, 2012. "Inverse Batschelet Distributions for Circular Data," Biometrics, The International Biometric Society, vol. 68(1), pages 183-193, March.
    11. Ameijeiras-Alonso, Jose & Gijbels, Irène & Verhasselt, Anneleen, 2022. "On a family of two–piece circular distributions," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    12. 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.
    13. 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.
    14. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    15. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    16. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    17. Sara Salvador & Riccardo Gatto, 2022. "Bayesian tests of symmetry for the generalized Von Mises distribution," Computational Statistics, Springer, vol. 37(2), pages 947-974, April.
    18. Toshihiro Abe & Hiroaki Ogata & Takayuki Shiohama & Hiroyuki Taniai, 2017. "Circular autocorrelation of stationary circular Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 275-290, October.
    19. 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.
    20. Ley, Christophe & Verdebout, Thomas, 2017. "Skew-rotationally-symmetric distributions and related efficient inferential procedures," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 67-81.

    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:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-019-00201-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.