6 Questions
The coefficient of upper tail dependence of X and Y is u = lim q1 P Y > G1(q) X > F1(q) . If u = 0 then X and Y are asymptotically __________ in the upper tail.
independent
If 0 < u 1, then X and Y are said to have upper tail __________.
dependence
The coefficient of lower tail dependence of X and Y is = lim q0 P(Y G1(q) X F1(q)). If = 0 then X and Y are asymptotically __________ in the lower tail.
independent
If 0 < 1, then X and Y are said to have lower tail __________.
dependence
The coefficients of upper and lower tail dependence of X and Y can be written respectively as u = 2 lim q1 1 C(q, q) 1 q and = lim q0 C(q, q) q Archimedean __________.
copulas
Theorem 6.9 states that = 2 lim q0 (q) (1(2(q))) can be expressed in terms of the generator function of an Archimedean __________.
copula
Learn about the concepts of upper and lower tail dependence in the context of continuous random variables. Explore how the coefficients λu and λℓ are calculated and their implications on the independence of the variables.
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