Probability and Statistics Index > Statistics Definitions > Leptokurtic

*Leptokurtic is directly related to kurtosis (a guide to how “peaked” your graph is), so you may want to read this article first: What is Kurtosis?*

A leptokurtic distribution has excess positive kurtosis, where the kurtosis is greater than 3. “Lepto-” means *slender*, referring to the tall, slender peak in the distribution. The distribution looks like a normal distribution at first glance. The following illustration^{1} shows a leptokurtic distribution along with a normal distribution (dotted line).

As you can probably tell, a leptokurtic distribution has a sharper peak around the mean. In other words, there are more values closer to the mean. The opposite is a platykurtic distribution, which is broad and flat like the uniform distribution.

## The Leptokurtic T-Test

The Student’s t-test is an example of a leptokurtic distribution. The t-distribution has fatter tails than the normal (you can also look at the first image above to see the fatter tails). Therefore, the critical values in a Student’s t-test will be larger than the critical values from a z-test.

## Financial Markets

Kurtosis isn’t just a theory confined to mathematical textbooks; it has real life applications, especially in the world of economics. Fund managers usually focus on risks and returns, kurtosis (in particular if an investment is lepto- or platy-kurtic). According to stock trader and analyst Michael Harris, a leptokurtic return means that risks are coming from outlier events. This would be a stock for investors willing to take extreme risks. For example, real estate (with a kurtosis of 8.75) and High Yield US bonds (8.63) are high risk investments while Investment grade US bonds (1.06) and Small cap US stocks (1.08) would be considered safer investments.

But kurtosis tells you nothing about the peak of the distribution. See http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4321753/pdf/nihms-599845.pdf

Thanks for your comment, Peter. It’s become widespread to think of kurtosis as peakedness. This could possibly be because it’s much easier for the average student to visualize what a tall or flat-peaked distribution looks like (as opposed to a distribution with fat tails or thin tails). I did add a little more info about the fact that fat tails leads to a flatter peak. I hope that clarifies it!