Kurtosis

In probability theory and statistics, kurtosis (from the Greek word kurtos, meaning bulging) is a measure of the "peakedness" of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestly-sized deviations.
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Measures the fatness of the tails of a probability distribution. A fat tailed distribution has higher than normal chances of a big positive or negative realization. Kurtosis should not be confused with skewness which measures the fatness of one tail. Kurtosis is sometimes refered to as the volatility of volatility.

Kurtosis (the term first used by Pearson, 1905) measures the "peakedness" of a distribution. If the kurtosis is clearly different than 0, then the distribution is either flatter or more peaked than normal; the kurtosis of the normal distribution is 0. Kurtosis is computed as:
Kurtosis = [n*(n+1)*M4-3*M2*M2*(n-1)]/[(n-1)*(n-2)*(n-3)* 4]
where
Mj is equal to (xi-Meanx)j
n is the valid number of cases
4 is the standard deviation (sigma) raised to the fourth power
See also, Descriptive Statistics .

kurtosis

kurtosis
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