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A note on a measure of asymmetry

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  • Andreas Eberl

    (Karlsruher Institut für Technologie (KIT))

  • Bernhard Klar

    (Karlsruher Institut für Technologie (KIT))

Abstract

A recently proposed measure of asymmetry (Patil et al. in Stat Papers 53: 971–985, 2012) is analyzed in detail. Several examples illustrate the peculiar behavior of this measure $$\eta $$ η as a measure of asymmetry or skewness. These findings are supported by theoretical considerations. Specifically, $$\eta $$ η is revealed to be a measure of similarity with the exponential distribution rather than an asymmetry measure. To illustrate this, we consider a related goodness of fit test for exponentiality. Moreover, we show that the partly erratic behavior of $$\eta $$ η also has a negative impact on the estimation of the measure.

Suggested Citation

  • Andreas Eberl & Bernhard Klar, 2021. "A note on a measure of asymmetry," Statistical Papers, Springer, vol. 62(3), pages 1483-1497, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01145-4
    DOI: 10.1007/s00362-019-01145-4
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    References listed on IDEAS

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    1. 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.
    2. Jun Zhang & Jing Zhang & Xuehu Zhu & Tao Lu, 2018. "Testing symmetry based on empirical likelihood," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(13), pages 2429-2454, October.
    3. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    4. Norbert Henze & Simos G. Meintanis, 2005. "Recent and classical tests for exponentiality: a partial review with comparisons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 29-45, February.
    5. P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
    6. 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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    Cited by:

    1. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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