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Skewness and kurtosis analysis for non-Gaussian distributions

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  • Celikoglu, Ahmet
  • Tirnakli, Ugur

Abstract

In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0

Suggested Citation

  • Celikoglu, Ahmet & Tirnakli, Ugur, 2018. "Skewness and kurtosis analysis for non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 325-334.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:325-334
    DOI: 10.1016/j.physa.2018.02.035
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    Cited by:

    1. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    2. Gala, Kaushik & Schwab, Andreas & Mueller, Brandon A., 2024. "Star entrepreneurs on digital platforms: Heavy-tailed performance distributions and their generative mechanisms," Journal of Business Venturing, Elsevier, vol. 39(1).
    3. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    4. Gonçalves, Alan D.S. & Fernandes, Leonardo H.S. & Nascimento, Abraão D.C., 2022. "Dynamics diagnosis of the COVID-19 deaths using the Pearson diagram," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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