We can derive the mean excess from the pdf, 1/(b-u). This is a uniform distribution with parameters b and u. Hence mean = 1/2*(b+u) As u increase, mean increase. The answer to this question mention that mean excess will decrease linearly. This part seems to contradict what I have derived as above. Anyone knows the explanation for this?
Hi. I think the XS distribution (ie Y=X-u) is uniform U(0,b-u) not (u,b). So, you end up with mean of (b-u)/2 as expected. Intuitively this must be true. As u increases the distance to b decreases, so the average distance to b decreases (note that the mean of the losses > u does increase. The mean of the losses > u is (b+u)/2, but as we are interested in the excess loss, we have (b+u)/2-u)