IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v53y2012i4p971-985.html
   My bibliography  Save this article

A measure of asymmetry

Author

Listed:
  • P. Patil
  • P. Patil
  • D. Bagkavos

Abstract

It is a general practice to make assertions about the symmetry or asymmetry of a probability density function based on the coefficients of skewness. Since most of the coefficients of skewness are designed to be zero for a symmetric density, they overall do provide an indication of symmetry. However, skewness is primarily influenced by the tail behavior of a density function, and the skewness coefficients are designed to capture this behavior. Thus they do not calibrate asymmetry in the density curves. We provide a necessary condition for a probability density function to be symmetric and use that to measure asymmetry in a continuous density curve on the scale of −1 to 1. We show through examples that the proposed measure does an admirable job of capturing the visual impression of asymmetry of a continuous density function. Copyright Springer-Verlag 2012

Suggested Citation

  • P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:971-985
    DOI: 10.1007/s00362-011-0401-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-011-0401-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-011-0401-6?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. Boshnakov, Georgi N., 2007. "Some measures for asymmetry of distributions," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1111-1116, June.
    2. Frank Critchley & M. C. Jones, 2008. "Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 415-437, September.
    3. Xiaojun, Li & Morris, Joel M., 1991. "On measuring asymmetry and the reliability of the skewness measure," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 267-271, September.
    4. Evarist Giné & David M. Mason, 2008. "Uniform in Bandwidth Estimation of Integral Functionals of the Density Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 739-761, December.
    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. Andreas Eberl & Bernhard Klar, 2021. "A note on a measure of asymmetry," Statistical Papers, Springer, vol. 62(3), pages 1483-1497, June.
    2. Xu, Zhongxiang & Chevapatrakul, Thanaset & Li, Xiafei, 2019. "Return asymmetry and the cross section of stock returns," Journal of International Money and Finance, Elsevier, vol. 97(C), pages 93-110.
    3. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    4. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.

    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. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.
    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. J. Rosco & M. Jones & Arthur Pewsey, 2011. "Skew t distributions via the sinh-arcsinh transformation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 630-652, November.
    4. A. Arriaza & A. Crescenzo & M. A. Sordo & A. Suárez-Llorens, 2019. "Shape measures based on the convex transform order," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 99-124, January.
    5. Giri Parameswaran & Hunter Rendleman, 2022. "Redistribution under general decision rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(1), pages 159-196, February.
    6. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    7. Mokkadem, Abdelkader & Pelletier, Mariane, 2020. "Online estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 166(C).
    8. Frank Critchley & M. C. Jones, 2008. "Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 415-437, September.
    9. I. H. Tajuddin, 1999. "A comparison between two simple measures of skewness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(6), pages 767-774.
    10. Robert Staudte, 2014. "Inference for quantile measures of skewness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 751-768, December.
    11. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    12. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    13. Rubio, Francisco Javier & Steel, Mark F. J., 2014. "Bayesian modelling of skewness and kurtosis with two-piece scale and shape transformations," MPRA Paper 57102, University Library of Munich, Germany.
    14. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
    15. José E. Chacón & Carlos Tenreiro, 2012. "Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 523-548, September.
    16. Andreas Eberl & Bernhard Klar, 2022. "Expectile‐based measures of skewness," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 373-399, March.
    17. Christopher Withers & Saralees Nadarajah, 2011. "Nonparametric confidence intervals for the integral of a function of an unknown density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 943-966.
    18. Andreas Eberl & Bernhard Klar, 2021. "A note on a measure of asymmetry," Statistical Papers, Springer, vol. 62(3), pages 1483-1497, June.
    19. Giovanni Campisi & Luca La Rocca & Silvia Muzzioli, 2023. "Assessing skewness in financial markets," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 48-70, February.
    20. Irène Gijbels & Rezaul Karim & Anneleen Verhasselt, 2020. "Response to the Letter to the Editor on ‘On Quantile‐based Asymmetric Family of Distributions: Properties and Inference’," International Statistical Review, International Statistical Institute, vol. 88(3), pages 797-801, December.

    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:stpapr:v:53:y:2012:i:4:p:971-985. 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.