What is a leptokurtic distribution?

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What is a leptokurtic distribution?

A leptokurtic distribution is fat-tailed, meaning that there are a lot of outliers.

Leptokurtic distributions are more kurtotic than a normal distribution. They have:

  • A kurtosis of more than 3
  • An excess kurtosis of more than 0

Leptokurtosis is sometimes called positive kurtosis, since the excess kurtosis is positive.

Note
The “lepto” in “leptokurtosis” comes from the Greek word leptós, which means narrow. Like platykurtosis, this is a misnomer because it defines kurtosis in terms of “peakedness” instead of tailedness. 

A trick to remember the meaning of “leptokurtic” is to think of a leaping kangaroo with a fat tail.

Leptokurtic distribution example

Imagine that four astronomers are all trying to measure the distance between the Earth and Nu2 Draconis A, a blue star that’s part of the Draco constellation. Each of the four astronomers measures the distance 100 times, and they put their data together in the same dataset:

Leptokurtic distribution

The frequency distribution (shown by the gray bars) doesn’t follow a normal distribution (shown by the dotted green curve). Instead, it approximately follows a Laplace distribution (shown by the blue curve). Laplace distributions are leptokurtic.

The astronomers calculate that the kurtosis of the sample is 6.54 and its excess kurtosis is 3.54. They conclude that the distribution is leptokurtic.

Leptokurtic distributions have frequent outliers. The distribution of the astronomers’ measurements has more outliers than you would expect if the distribution were normal, with several extreme observations that are less than 50 or more than 150 light-years.

Note
If you look closely at the graph above, you’ll notice that on the far left and right sides of the distribution—the tails—the space below the Laplace distribution curve (blue) is slightly thicker than the space below the normal distribution curve (green). This is what is meant by “fat tails.”

Published by Henry