A note on a measure of asymmetry

Andreas Eberl () and Bernhard Klar ()
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Andreas Eberl: Karlsruher Institut für Technologie (KIT)
Bernhard Klar: Karlsruher Institut für Technologie (KIT)

Statistical Papers, 2021, vol. 62, issue 3, No 17, 1483-1497

Abstract: 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.

Keywords: Asymmetry measure; Skewness; Correlation; Characterization of exponentiality; Goodness of fit test (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01145-4

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