On the meaning and use of kurtosis.

Abstract

For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurtosis is illustrated with well-known distributions, and aspects of its interpretation a d misinterpretation are discussed. The role of kurtosis in testing univariate and multivariate normality; as a measure of departures from normality; in issues of robustness, outliers, and bimodality; in generalized tests and estimators, as well as limitations of and alternatives to the kurtosis measure [32, are discussed. It is typical ly noted in introductory statistics courses that distributions can be characterized in terms of central tendency, variability, and shape. With respect o shape, virtually every textbook defines and illustrates kewness. On the other hand, another as-pect of shape, which is kurtosis, is either not discussed or, worse yet, is often described or illustrated incor-rectly. Kurtosis is also frequently not reported in re-search articles, in spite of the fact that virtually every statistical package provides a measure of kurtosis. This occurs most likely because kurtosis is not well understood and because the role of kurtosis in various aspects of statistical analysis is not widely recognized. The purpose of this article is to clarify the meaning of kurtosis and to show why and how it is useful. On the Mean ing o f Kurtosis Kurtosis can be formally defined as the standard-ized fourth population moment about the mean, E (X- IX)4 IX4

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