Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The general form or a quantity indicative of the general form of a statistical frequency curve near the mean of the distribution.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 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
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 techtalk to minimum, but this one had a few eyeglazers: “Probability density function” and “variance and the kurtosis of the distribution changes”

Or traditional bell curves do not apply because of nonnormal 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 JarqueBera test based on the sample kurtosis and skewness.
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