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Kurtosis is a statistical measure that describes the shape of a distribution’s tails in relation to its central peak. It measures the degree of peakedness or flatness of a distribution compared to a normal distribution. In some cases, the kurtosis value can be negative, indicating that the distribution has thinner tails and a less pronounced central peak compared to a normal distribution. This is known as a platykurtic distribution and is a rare occurrence in most statistical analyses. While it is possible for kurtosis to be negative, it is generally considered a non-standard result and may require further investigation to understand its implications.
Can Kurtosis Be Negative?
In statistics, kurtosis is used to describe the shape of a probability distribution.
Specifically, it tells us the degree to which data values cluster in the tails or the peak of a distribution.
The kurtosis for a distribution can be negative, equal to zero, or positive.
Zero Kurtosis
If a distribution has a kurtosis of 0, then it is equal to the normal distribution which has the following bell-shape:
Positive Kurtosis
If a distribution has positive kurtosis, it is said to be leptokurtic, which means that it has a sharper peak and heavier tails compared to a normal distribution.
This simply means that fewer data values are located near the mean and more data values are located on the tails.
The most well-known distribution that has a positive kurtosis is the t distribution, which has a sharper peak and heaver tails compared to the normal distribution.
Negative Kurtosis
If a distribution has negative kurtosis, it is said to be platykurtic, which means that it has a flatter peak and thinner tails compared to a normal distribution.
This simply means that more data values are located near the mean and less data values are located on the tails.
One extreme example of a distribution that has a negative kurtosis is the , which has no peak at all and is a completely flat distribution.
When to Use Kurtosis in Practice
So, if we see that the kurtosis is positive then we know we’re working with a distribution that has fewer data values located near the center and more data values that are spread out along the tails.
Conversely, if we see that the kurtosis is negative then we know we’re working with a distribution that has more data values located near the center and less data values in the tails.
Additional Resources
To find the skewness and kurtosis for a given distribution, you can enter the raw data values into this Skewness and Kurtosis Calculator, which will tell you both the skewness and kurtosis for the distribution.
One of the most popular statistical tests that is used to determine whether or not a particular distribution has skewness and kurtosis that matches a normal distribution is the Jarque Bera Test.
Khan Academy also hasa nice video seriesthat describes how to classify the shapes of distributions.