Sunday, April 22, 2012

kurtosis -- thick tail AND slender

All normal distributions have kurtosis == 3.000. Any positive "excess kurtosis" is known as leptokurtic and is a sign of thick tail.

The word leptokurtic initially means slender -- in a histogram, the center bar is higher, i.e. higher concentration towards the mean. To my surprise, the extreme left/right bars are also __higher___, indicating thick tails. To compensate, the rest of the bars must be shorter, since all the bars in a histogram must add up to 100%.

In short, excess kurtosis means 1) slender and 2) thick tail.

Thick tail is more important to many users as thick tail means more unexpected extreme deviations (from mean) than in the Normal distribution. Thick tail is unexplainable by Normal distribution and indicates a different, unidentified distribution.

However, the "Slender" feature is more visible and is the meaning of "leptokurtic". The thick tail is almost invisible unless plotted logarithmically -- see http://en.wikipedia.org/wiki/Kurtosis

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