A note on a measure of asymmetry

  • Andreas Eberl
  • Bernhard KlarEmail author
Regular Article


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 \(\eta \) as a measure of asymmetry or skewness. These findings are supported by theoretical considerations. Specifically, \(\eta \) 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 \(\eta \) also has a negative impact on the estimation of the measure.


Asymmetry measure Skewness Correlation Characterization of exponentiality Goodness of fit test 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für StochastikKarlsruher Institut für Technologie (KIT)KarlsruheGermany

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