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Some measures for asymmetry of distributions

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  • Boshnakov, Georgi N.

Abstract

We propose several measures, functional and scalar, for asymmetry of distributions by comparing the behavior of probability densities to the right and left of the mode(s) and show how to generate classes of equivalent distributions from a given distribution, allowing for varying asymmetry but retaining some information theoretic properties of the original distribution, such as the entropy.

Suggested Citation

  • Boshnakov, Georgi N., 2007. "Some measures for asymmetry of distributions," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1111-1116, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:11:p:1111-1116
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    References listed on IDEAS

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    1. Boshnakov, Georgi N., 2003. "Confidence characteristics of distributions," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 353-360, July.
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    Cited by:

    1. 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.
    2. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    3. 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.
    4. 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.
    5. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    6. P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
    7. 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.
    8. 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.

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