Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun A quantity indicating how sharply a probability distribution function increases and decreases around the distribution's mean.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun statistics A measure of "peakedness" of a probability distribution, defined as the fourth cumulant divided by the square of the variance of the probability distribution.

Etymologies

from The American Heritage® Dictionary of the English Language, 4th Edition

[Greek kurtōsis, bulging, curvature, from kurtoun, to make bulge, from kurtos, convex; see sker- in Indo-European roots.]

from Wiktionary, Creative Commons Attribution/Share-Alike License

From Ancient Greek κύρτωσις ("bulging, convexity"), from κυρτός (kurtos, "bulging").

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Examples

  • Moreover, the central limit theorem of probability theory does not apply in this context because empirical evidence shows that a constant standard deviation is an inaccurate measure of investment risk, due to the fact that investment performance, is typically skewed and exhibits kurtosis.

    Redefining Investor Risk 2010

  • I presume there was minimal kurtosis in these distributions.

    Seven-Year WMAP Results: No, They're NOT Anomalies | Universe Today 2010

  • Moreover, the central limit theorem of probability theory does not apply in this context because empirical evidence shows that a constant standard deviation is an inaccurate measure of investment risk, due to the fact that investment performance, is typically skewed and exhibits kurtosis.

    Redefining Investor Risk 2010

  • There is a kurtosis measure, a fourth moment as standard deviation is a second moment, for this variation.

    A Dark, Misleading Force Sean 2007

  • Normally they keep the tech-talk to minimum, but this one had a few eye-glazers: “Probability density function” and “variance and the kurtosis of the distribution changes”

    Unthreaded #19 « Climate Audit 2007

  • I would guess that a chi square goodness of fit test or a kurtosis/skewness test for normality would not eliminate a Poisson and/or a normal distribution as applying here without the sinusoidal correction.

    Paul Linsay's Poisson Fit « Climate Audit 2007

  • Or traditional bell curves do not apply because of non-normal distributions were distribution shapes tested for skew, kurtosis, etc?

    IPCC Review Comments Now Online « Climate Audit 2007

  • The variates not the observations have the same mean, variance, skew, kurtosis, etc.

    Paul Linsay's Poisson Fit « Climate Audit 2007

  • Further to #36: Thinking about this some more, the options point implies that we are interested not just in the mean and variance of the distribution but also the “tails” — skewness, kurtosis etc.

    Gerry Browning: Numerical Climate Models « Climate Audit 2006

  • The shape of the curve is very important kurtosis.

    Whitfield subCommittee II: Mann under fire « Climate Audit 2006

Comments

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  • Distributions with long tails are called leptokurtic; distributions with short tails are called platykurtic. Normal distributions have zero kurtosis.

    David M. Lane et al., Introduction to Statistics (I don't see the date), p. 669

    April 7, 2018