Hello I have a question on the upper tail dependence formula. From the notes, P(F(x)>u, F(y)>u)=C bar(1-u, 1-u) May I know the meaning of C bar(u, u)? From the above, I have derived the below. Is the equation below correct and what does it mean? C bar(u, u) = P(F(x)>1-u, F(y)>1-u)
Hi Alex My brain is sore from thinking about this! As an example, let's take u = 0.05 u = F(x) = F(y) 0.05 = u = P(X < x) = P(Y < y) 0.95 = 1-u = P(X > x) = P(Y > y) C(u, u) = P(F(x)<u, F(y)<u) This is the probability that X and Y take values in the lower 5% of the distribution. C(1-u, 1-u) = P(F(x)<1-u, F(y)<1-u) This is the probability that X and Y take values in the lower 95% of the distribution. C bar(1-u, 1-u) = P(F(x)>u, F(y)>u) {Result from Page 19 of Module 18) C bar is the survival probability. This is the probability both X and Y take values in the upper 95% of the distribution, ie that they survive the first 5%! C bar(u, u) = P(F(x)>1-u, F(y)>1-u) C bar is the survival probability. This is the probability both X and Y take values in the upper 5% of the distribution, ie that they survive the first 95%! Is this OK? Anna
