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M18 Upper tail dependence

A

ALEX_AK

Member
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
 
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