Definitions
American Heritage® Dictionary of the English Language, Fourth Edition
- n. The general form or a quantity indicative of the general form of a statistical frequency curve near the mean of the distribution.
Wiktionary
- n. 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
- Greek kurtōsis, bulging, curvature, from kurtos, convex; see sker-2 in Indo-European roots.
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.”
“I presume there was minimal kurtosis in these distributions.”
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“There is a kurtosis measure, a fourth moment as standard deviation is a second moment, for this variation.”
“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””
“Or traditional bell curves do not apply because of non-normal distributions were distribution shapes tested for skew, kurtosis, etc?”
“The variates not the observations have the same mean, variance, skew, kurtosis, etc.”
“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.”
“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.”
“The shape of the curve is very important kurtosis.”
“I am more familiar with a chi squared goodness of fit test of the binned distribution compared to that for a nomal distribution and/or something like a Jarque-Bera test based on the sample kurtosis and skewness.”
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