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Karl Pearson and the Origin of Kurtosis

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  • Anna M. Fiori
  • Michele Zenga

Abstract

Although the kurtosis index proposed by Karl Pearson in 1905 is introduced in statistical textbooks at all levels, the measure is not easily interpreted and has been a subject of considerable debate. In this study, the theoretical development of kurtosis is surveyed from a historical perspective of Pearson's work on evolution. It surprisingly emerges that there was no emphasis in Pearson's papers on kurtosis as measuring (in part) tail heaviness. However, it is found that Pearson used to frequently adjust the formalisation of kurtosis depending on his changing needs. This complex development partly explains the confusion that would surround kurtosis in subsequent literature. Our conclusion is that most misunderstandings arise from improper use of the kurtosis coefficient outside the Pearson system of frequency curves.

Suggested Citation

  • Anna M. Fiori & Michele Zenga, 2009. "Karl Pearson and the Origin of Kurtosis," International Statistical Review, International Statistical Institute, vol. 77(1), pages 40-50, April.
    • Handle: RePEc:bla:istatr:v:77:y:2009:i:1:p:40-50
    DOI: 10.1111/j.1751-5823.2009.00076.x
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    File URL: https://doi.org/10.1111/j.1751-5823.2009.00076.x
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    References listed on IDEAS

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    1. Anna Maria Fiori & Michele Zenga, 2005. "The meaning of kurtosis, the influence function and an early intuition by L. Faleschini," Statistica, Department of Statistics, University of Bologna, vol. 65(2), pages 135-144.
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    Cited by:

    1. Claudio Giovanni Borroni & Lucio De Capitani, 2022. "Some measures of kurtosis and their inference on large datasets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 573-607, December.
    2. Nicholas J. Cox, 2010. "Speaking Stata: The limits of sample skewness and kurtosis," Stata Journal, StataCorp LP, vol. 10(3), pages 482-495, September.
    3. J. Martin van Zyl, 2018. "An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions," Papers 1811.00476, arXiv.org, revised Nov 2018.
    4. Anna Maria Fiori, 2020. "On firm size distribution: statistical models, mechanisms, and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 447-482, September.
    5. Yeboah Asuamah, Samuel, 2015. "An econometric modelling of government activities-total energy demand nexus for Ghana," MPRA Paper 83489, University Library of Munich, Germany.
    6. Perepolkin, Dmytro & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an, Center for Open Science.
    7. Claudio Giovanni Borroni, 2009. "Understanding Karl Pearson's Influence on Italian Statistics in the Early 20th Century," International Statistical Review, International Statistical Institute, vol. 77(1), pages 81-95, April.
    8. Eugene Seneta, 2009. "Karl Pearson in Russian Contexts," International Statistical Review, International Statistical Institute, vol. 77(1), pages 118-146, April.

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