Many incorrect interpretations of kurtosis that involve notions of peakedness have been given.
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So it gives the peakedness ( width of peak ) of the given spectrum.
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One is that kurtosis measures both the " peakedness " of the distribution and the heaviness of its tail.
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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 ).
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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 ).
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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.
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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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