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Excess Kurtosis

The excess kurtosis = kurtosis - 3.  This results in the normal distribution having an excess kurtosis of zero.  An excess kurtosis above 0 indicates the tails are heavier than the normal distribution.  An excess kurtosis below 0 indicates the tails are lighter than the normal distribution.  An excess kurtosis value of 1 and above or -1 and below represents a sizable departure from normality.  The formula used for estimating the excess kurtosis from a set of data is:



where n is the sample size, represents the data points, is the average and S is the standard deviation.