In probability theory, the tail dependence of a pair of random variables is a measure of their comovements in the tails of the distributions.
Random variables that appear to exhibit no correlation can show tail dependence in extreme deviations.
For instance, it is a stylized fact of stock returns that they commonly exhibit tail dependence.
, that is, the inverse of the cumulative probability distribution function for q.
The upper tail dependence is defined analogously as