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Inference via the Skewness‐Kurtosis Set

Chris A. J. Klaassen & Bert van Es

International Statistical Review2025https://doi.org/10.1111/insr.70007article
AJG 3ABDC A
Weight
0.41

Abstract

Summary Kurtosis minus squared skewness is bounded from below by 1, but for unimodal distributions, this parameter is bounded by 189/125. In some applications, it is natural to compare distributions by comparing their kurtosis‐minus‐squared‐skewness parameters. The asymptotic behavior of the empirical version of this parameter is studied here for i.i.d. random variables. The result may be used to test the hypothesis of unimodality against the alternative that the kurtosis‐minus‐squared‐skewness parameter is less than 189/125. However, such a test has to be applied with care, because this parameter can take arbitrarily large values, also for multimodal distributions. We also present a test for symmetric unimodality. Simulation results are presented and for three classes of distributions the skewness‐kurtosis sets are described in detail.

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https://doi.org/https://doi.org/10.1111/insr.70007

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@article{chris2025,
  title        = {{Inference via the Skewness‐Kurtosis Set}},
  author       = {Chris A. J. Klaassen & Bert van Es},
  journal      = {International Statistical Review},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1111/insr.70007},
}

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Evidence weight

0.41

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.25 × 0.4 = 0.10
M · momentum0.55 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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