Abstract
The consequences of substituting the denominator Q3(p) − Q1(p) by Q2 − Q1(p) in Groeneveld’s class of quantile measures of kurtosis (γ2(p)) for symmetric distributions, are explored using the symmetric influence function. The relationship between the measure γ2(p) and the alternative class of kurtosis measures κ2(p) is derived together with the relationship between their influence functions. The Laplace, Logistic, symmetric Two-sided Power, Tukey and Beta distributions are considered in the examples in order to discuss the results obtained pertaining to unimodal, heavy tailed, bounded domain and U-shaped distributions.
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