What does kurtosis measure in relation to a distribution?

Kurtosis is a statistical measure that describes the shape of a distribution, specifically focusing on the "peakedness." It indicates how sharply peaked or flat the top of the distribution is compared to a normal distribution. A higher kurtosis value means a sharper peak, which indicates that more of the data is concentrated around the mean, along with heavier tails. This suggests a higher probability of extreme values occurring. Conversely, a lower kurtosis indicates a flatter peak, suggesting a more uniform distribution of data points across the range.

Understanding kurtosis is important in risk management as it helps analysts understand the likelihood of extreme outcomes, which is crucial for evaluating risks. This measure complements other statistical descriptors like mean and variance to provide a complete picture of the distribution’s characteristics.