Which distribution is known for having fatter tails and a higher probability of extreme values?

The leptokurtic distribution is characterized by its fatter tails compared to a normal distribution, which indicates a higher likelihood of extreme values. In a leptokurtic distribution, the peak is more pronounced, and there is a greater concentration of data points near the mean, along with a significant number of observations in the tails. This means that in situations modeled by a leptokurtic distribution, there are more instances of unusually high or low values.

In contrast, a mesokurtic distribution represents a normal distribution, which has a kurtosis value of 3 and does not exhibit the same level of tail thickness or propensity for extreme values as a leptokurtic distribution. The platykurtic distribution, on the other hand, has thinner tails and a lower likelihood of extreme values. Therefore, when looking for a distribution associated with fatter tails and an increased probability of extreme outcomes, the leptokurtic distribution is the appropriate choice.