An Analysis of Quantile Measures of Kurtosis: Center and Tails

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The consequences of substituting the denominator Q 3(p) - Q 1(p) by Q 2 - Q 1(p) in Groeneveld's class of quantile measures of kurtosis (γ 2(p)) for symmetric distributions, are explored using the symmetric influence function. The relationship between the measure γ 2(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.