Leptokurtic Distribution: The 3 Types of Kurtosis Explained

A leptokurtic distribution is a type of statistical graph with positive excess kurtosis over three. The term leptokurtic derives from the Greek words “lepto” (meaning “narrow”) and “kurtos” (meaning “bulging”). Leptokurtosis is one of the three main types of kurtosis alongside platykurtosis and mesokurtosis.

This means frequency distributions of this ilk have a greater number of variations in the tails of data on both sides of the information’s peak. In other words, there are more statistical variations and less of a solid mean when it comes to certain outcomes. Put simply, leptokurtic distributions have a more unpredictable story to tell than you would see in comparison to a normal distribution.

The Laplace distribution is a prominent example of leptokurtosis in action. In this distribution, the data reveals a much higher degree of outliers than you would expect in other typical statistical alternatives like Gaussian distributions.

Kurtosis refers to the number of deviations from the standard mean you can see in the tails of the distribution. In mathematical equations, you might see kurtosis abbreviated as Kurt. Kurtosis shows up in how fat or slim the tails are in statistical diagrams. As you compare these tails to the peak of the diagram, you get a general idea of what the kurtosis is for any specific set of data.

In descriptive statistics, kurtosis can help you gain a better understanding of the data you are reviewing. Here are three key elements to observe:

1. 1. Additional variables: The accurate characterization of kurtosis requires you to look at other aspects of statistical data as well. Mathematicians call kurtosis the fourth moment of a distribution, implying there are three others you must also take into account. These first three moments are—in order from first to third—mean (the average of all the data), variance (the spread between data points), and skewness (the deviation from a normal distribution).
2. 2. Peaks: Kurtosis has just as much to do with the peak of a diagram as it does with its tails. For instance, while statisticians primarily define leptokurtosis in terms of its fat tails, it can also manifest in a higher peak. The peakedness of a distribution helps you understand how many data points fall among the average as opposed to existing as outliers. Comparing averages against outliers is one of the primary ways to determine kurtosis.
3. 3. Tails: As you look at the tails of your dataset, you get to the core of kurtosis. If these tails are full of outliers (and have fatter tails as a result), you have an excess of kurtosis on your hands. The same goes in reverse—fewer outliers means less kurtosis. The closer your tails are to mimicking the pattern of a standard deviation, the more likely you are to have a regular amount of kurtosis.

Leptokurtic distributions are the direct opposite of their platykurtic counterparts. The former has positive excess kurtosis (upward of 3.0) while the latter has negative excess kurtosis (downward of 3.0). This negative value makes platykurtic distributions less likely to depict outlier events in the tails of the data they depict. This generally translates to statistical data indicating a very predictable and typical flow of events and variables (sometimes called a uniform distribution).

Mesokurtic distributions have low kurtosis in comparison to leptokurtic ones, but they clock in above platykurtic ones as well. They have a kurtosis of 3.0, meaning they fit the normal curve of typical statistical data. If a dataset achieves mesokurtosis, it indicates the tails in the information include the typical amount of outliers one would expect. Rather than seeming too “fat” or “thin,” these tails look the same as you would expect them to on a traditional example of statistical analysis.

Suppose an investor wants to see how much risk exists in his stock portfolio. A leptokurtic distribution (meaning a high amount of extreme outliers and a less reliable central average) would indicate the portfolio is high-risk, meaning there’s just as much of a likelihood for big rewards as big losses in the tails of the dataset. You can also contrast this with a platykurtic portfolio, which would indicate less than average risk, and with a mesokurtic one, which would indicate the typical level one could reasonably expect.

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