Many incorrect interpretations of kurtosis that involve notions of peakedness have been given.
2.
So it gives the peakedness ( width of peak ) of the given spectrum.
3.
One is that kurtosis measures both the " peakedness " of the distribution and the heaviness of its tail.
4.
Where this kind of spectrum exists, and voters prefer candidates who are closest to their own position on the spectrum, there is a Condorcet winner ( Black's Single-Peakedness Theorem ).
5.
The description of kurtosis as a measure of the " peakedness " ( or " heavy tails " ) of the probability distribution, is strictly applicable to unimodal distributions ( for example the normal distribution ).
6.
This example makes it clear that data near the " middle " or " peak " of the distribution do not contribute to the kurtosis statistic, hence kurtosis does not measure " peakedness . " It is simply a measure of the outlier, 999 in this example.
7.
Balanda and MacGillivray assert that the standard definition of kurtosis " is a poor measure of the kurtosis, peakedness, or tail weight of a distribution " and instead propose to " define kurtosis vaguely as the location-and scale-free movement of probability mass from the shoulders of a distribution into its center and tails ".
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