Leptokurtic distributions describe any statistical distribution with a higher degree of peakedness than the normal distribution. The term "leptokurtic" comes from the Greek for "slender kurtosis", emphasizing the fact that these distributions have thinner, sharper peaks than normal distributions. They are considered to be "fat-tailed" distributions due to the presence of extreme values in the tails.

In terms of shape, leptokurtic distributions have higher peaks and a larger spread than normal distributions. The properties of the variance, mean, and skewness generally remain the same, while the kurtosis increases. The use of the kurtosis, usually denoted by Greek letter γ, is helpful when comparing distributions. A leptokurtotic distribution will have γ > 3 as compared to the normal distribution which has γ = 3.

The leptokurtic distribution has a greater likelihood of extreme events than normal distributions. This means that investors looking for larger returns (or higher risk) can focus on investments whose returns follow a leptokurtic distribution. This carries with it the increased chance of rare, extreme events occurring—both positive and negative. That’s why investors should be aware of this when allocating resources.

The concept of leptokurtic distributions has broad implications. It can be used to model the behavior of a wide variety of data sets, such as stock prices, real estate values, election vote percentages, etc. By using leptokurtic distributions, investors and analysts can better focus on the most probable outcome, as well as the chances for less frequent, but potentially more profitable, events.

In conclusion, leptokurtic distributions can be used as an analytical tool to better understand the behavior of different data sets. Investors and analysts should be aware of this property of leptokurtic distributions and use it when looking to identify potential opportunities with larger returns, but more importantly, be aware of the higher risk associated with the chances of extreme events occurring.