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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

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

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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
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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