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Convex transformations: A new approach to slcewness and kurtosis

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  • W. R. van Zwet

Abstract

In dit artikel worden een tweetal orde‐relaties voor waarschijnlijkheidsverde‐lingen voorgesteld, die ‐ beter dan de klassieke maten gebaseerd op derde en vierde momenten ‐ aangeven wanneer een verdeling een grotere scheefheid of kurtosis bezit dan een andere verdeling. Voorts wordt een aantal karakterise‐ringen en toepassingen van deze orde‐relaties behandeld. Bewijzen worden in dit artikel niet gegeven; deze zijn te vinden in een meer uitgebreide, aan dit onder‐werp gewijde studie [5].

Suggested Citation

  • W. R. van Zwet, 1964. "Convex transformations: A new approach to slcewness and kurtosis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 18(4), pages 433-441, December.
    • Handle: RePEc:bla:stanee:v:18:y:1964:i:4:p:433-441
    DOI: 10.1111/j.1467-9574.1964.tb00530.x
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    Cited by:

    1. Joe, Harry & Ma, Chunsheng, 2000. "Multivariate Survival Functions with a Min-Stable Property," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 13-35, October.
    2. Sophocles P. Ioulianou & Michael J. Leiblein & Lenos Trigeorgis, 2021. "Multinationality, portfolio diversification, and asymmetric MNE performance: The moderating role of real options awareness," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 52(3), pages 388-408, April.
    3. Luís Cabral & Gonçalo Pacheco-de-Almeida, 2019. "Alliance Formation and Firm Value," Management Science, INFORMS, vol. 65(2), pages 879-895, February.
    4. Gajek, Leslaw & Rychlik, Tomasz, 1998. "Projection Method for Moment Bounds on Order Statistics from Restricted Families, : II. Independent Case," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 156-182, February.
    5. Giovanni Campisi & Luca La Rocca & Silvia Muzzioli, 2023. "Assessing skewness in financial markets," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 48-70, February.
    6. Yevgeniy Kovchegov, 2022. "A New Life of Pearson’s Skewness," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2896-2915, December.
    7. Childs, Aaron & Balakrishnan, N., 2002. "Series approximations for moments of order statistics using MAPLE," Computational Statistics & Data Analysis, Elsevier, vol. 38(3), pages 331-347, January.
    8. Rayner, G. D. & MacGillivray, H. L., 2002. "Weighted quantile-based estimation for a class of transformation distributions," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 401-433, June.
    9. Erich Lehmann, 2009. "Parametric versus nonparametrics: two alternative methodologies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 397-405.

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