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 \(\eta \) 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.
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Eberl, A., Klar, B. A note on a measure of asymmetry. Stat Papers 62, 1483–1497 (2021). https://doi.org/10.1007/s00362-019-01145-4
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DOI: https://doi.org/10.1007/s00362-019-01145-4