An analysis of quantile measures of kurtosis: center and tails |
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| Authors: | Samuel Kotz Edith Seier |
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| Institution: | (1) Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, USA;(2) Department of Mathematics, East Tennessee State University, Johnson City, TN 37614, USA |
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| Abstract: | 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.
The authors thank the referee for the careful review. |
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| Keywords: | Influence function Symmetric distributions Heavy-tailed distributions Groeneveld measure |
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