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Sharp inequalities between skewness and kurtosis

Author

Listed:
  • Rohatgi, Vijay K.
  • Székely, Gábor J.

Abstract

Denote by [alpha] and [beta] the skewness and kurtosis respectively of a distribution with finite fourth moment. We show that [alpha]2 [less-than-or-equals, slant] [beta] + 2. For unimodal distributions we prove that [alpha]2 [less-than-or-equals, slant] [beta] + , and for infinitely divisible distributions [alpha]2 [less-than-or-equals, slant] [beta].

Suggested Citation

  • Rohatgi, Vijay K. & Székely, Gábor J., 1989. "Sharp inequalities between skewness and kurtosis," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 297-299, September.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:4:p:297-299
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    Cited by:

    1. Silvano Vergura & Mario Carpentieri, 2017. "Statistics to Detect Low-Intensity Anomalies in PV Systems," Energies, MDPI, vol. 11(1), pages 1-12, December.
    2. Hong, Sung-Pil & Kim, Kyung min & Byeon, Geunyeong & Min, Yun-Hong, 2017. "A method to directly derive taste heterogeneity of travellers’ route choice in public transport from observed routes," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 41-52.
    3. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.
    4. Ogasawara, Haruhiko, 2017. "Extensions of Pearson’s inequality between skewness and kurtosis to multivariate cases," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 12-16.
    5. Yen Lee & David Kaplan, 2018. "Generating Multivariate Ordinal Data via Entropy Principles," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 156-181, March.
    6. Silvano Vergura, 2018. "A Statistical Tool to Detect and Locate Abnormal Operating Conditions in Photovoltaic Systems," Sustainability, MDPI, vol. 10(3), pages 1-15, February.
    7. Klein, Ingo & Doll, Monika, 2018. "Tests on asymmetry for ordered categorical variables," FAU Discussion Papers in Economics 03/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    8. Klaassen, Chris A. J. & Mokveld, Philip J. & van Es, Bert, 2000. "Squared skewness minus kurtosis bounded by 186/125 for unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 131-135, November.
    9. Teuscher, F. & Guiard, V., 1995. "Sharp inequalities between skewness and kurtosis for unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 257-260, February.
    10. Nicolae Tarbă & Mihai-Lucian Voncilă & Costin-Anton Boiangiu, 2022. "On Generalizing Sarle’s Bimodality Coefficient as a Path towards a Newly Composite Bimodality Coefficient," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    11. Silvano Vergura, 2018. "Hypothesis Tests-Based Analysis for Anomaly Detection in Photovoltaic Systems in the Absence of Environmental Parameters," Energies, MDPI, vol. 11(3), pages 1-18, February.
    12. Christopher C. Hadlock & J. Eric Bickel, 2019. "The Generalized Johnson Quantile-Parameterized Distribution System," Decision Analysis, INFORMS, vol. 16(1), pages 67-85, March.
    13. Liang, Zhenglin & Liu, Bin & Xie, Min & Parlikad, Ajith Kumar, 2020. "Condition-based maintenance for long-life assets with exposure to operational and environmental risks," International Journal of Production Economics, Elsevier, vol. 221(C).

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