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An analysis of quantile measures of kurtosis: center and tails

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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.

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Authors and Affiliations

  1. Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC, 20052, USA

    Samuel Kotz

  2. Department of Mathematics, East Tennessee State University, Johnson City, TN, 37614, USA

    Edith Seier

Authors
  1. Samuel Kotz
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  2. Edith Seier
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Correspondence to Samuel Kotz.

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The authors thank the referee for the careful review.

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Kotz, S., Seier, E. An analysis of quantile measures of kurtosis: center and tails. Stat Papers 50, 553–568 (2009). https://doi.org/10.1007/s00362-007-0101-4

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  • DOI: https://doi.org/10.1007/s00362-007-0101-4

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