Varentropy as a measure of fat-tailnedness
@nntaleb wrote in X about how varentropy could be a useful replacement for kurtosis as a measure of fait-tailedness.
Simple variability is a 1st order measure that measures the spread, and kurtosis measures the shape (thin vs fat tail) of the distribution. However, kurtosis breaks down when the tail gets fat enough, whereas varentropy survives even where kurtosis doesn’t, making it a more robust measure.
The little widget below lets you play with the tail index to see what happens to the four measures (variance/kurtosis, entropy/varentropy) when you vary the tail-index.