 # Kurtosis

Kurtosis:

Kurtosis measures the “heaviness of the tails” of a distribution (in compared to a normal distribution). Kurtosis is positive if the tails are “heavier” then for a normal distribution, and negative if the tails are “lighter” than for a normal distribution. The normal distribution has kurtosis of zero.

Kurtosis characterizes the shape of a distribution – that is, its value does not depend on an arbitrary change of the scale and location of the distribution. For example, kurtosis of a sample (or population) of temperature values in Fahrenheit will not change if you transform the values to Celsius (the mean and the variance will, however, change).

The kurtosis of a distribution or sample is equal to the 4th central moment divided by the 4th power of the standard deviation, minus 3.

To calculate the kurtosis of a sample:

i) subtract the mean from each value to get a set of deviations from the mean;

ii) divide each deviation by the standard deviation of all the deviations;

iii) average the 4th power of the deviations and subtract 3 from the result.

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