5. Consider the Clayton copula: C(u,v) = (u¯ª +v¯ α>0 -a - a for 0≤u≤1, 0≤v≤1, a. Show that the marginal distributions for u and v are uniform. b. Show that the pdf for this copula is always non-negative. c. Find the lower tail dependence, defined as λ₁ = lim Pr[X ≤ Fx' (u)|Y ≤ Fy'(u)] = u→0+ +0
5. Consider the Clayton copula: C(u,v) = (u¯ª +v¯ α>0 -a - a for 0≤u≤1, 0≤v≤1, a. Show that the marginal distributions for u and v are uniform. b. Show that the pdf for this copula is always non-negative. c. Find the lower tail dependence, defined as λ₁ = lim Pr[X ≤ Fx' (u)|Y ≤ Fy'(u)] = u→0+ +0
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![5. Consider the Clayton copula: C(u,v) = (u¯ª +v¯
α>0
-a
-
a for 0≤u≤1, 0≤v≤1,
a. Show that the marginal distributions for u and v are uniform.
b. Show that the pdf for this copula is always non-negative.
c. Find the lower tail dependence, defined as
λ₁ = lim Pr[X ≤ Fx' (u)|Y ≤ Fy'(u)] =
u→0+
+0<n
C(u,u)
и](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2Feef876f0-2c0b-4cdd-b991-9a241ac0c2e7%2Fueja1yi_processed.png&w=3840&q=75)
Transcribed Image Text:5. Consider the Clayton copula: C(u,v) = (u¯ª +v¯
α>0
-a
-
a for 0≤u≤1, 0≤v≤1,
a. Show that the marginal distributions for u and v are uniform.
b. Show that the pdf for this copula is always non-negative.
c. Find the lower tail dependence, defined as
λ₁ = lim Pr[X ≤ Fx' (u)|Y ≤ Fy'(u)] =
u→0+
+0<n
C(u,u)
и
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