Appreciate this might be a bit late given the exam is tomorrow! But I'm struggling to understand the gamma term in the GPD distribution. We're told in the CMP that for gamma (g) != 0 that G(x)= 1- (1+x/(gb))^{-g}, and for g=0 it is 1-exp(-x/b). I would expect that the distribution is continuous in gamma, but if you take the limit as g -> 0 you do not get the g=0 CDF. In fact it seems we get the exponential by taking gamma to infinity, not to zero, since (1+x/n)^n -> e^x as n -> infinity. Looking at wikipedia - https://en.wikipedia.org/wiki/Generalized_Pareto_distribution - it defines the GPD in terms of epsilon, where epsilon = 1/gamma. And in the exp CDF, we require epsilon = 0 (i.e. gamma = infinity). Am I missing something? Thanks
