# Math Help - Copula

1. ## Copula

Given two independent random variable X, Y such that

$
F(x) = P(X \leq x) = 1-e^{-\gamma x},\ F(y) = P(Y \leq y)= 1-e^{-\gamma y}
$

how could be demonstrated through Copula with uniform distributions that

$
C(u,v) = P(X \leq x, Y \leq y) = u + v -1 + \left[ (1-u)^{-1/\gamma} + (1-v)^{-1/\gamma} - 1\right]^{-\gamma}
$

or, alternatively that

$
C(1-u,1-v) = P(X > x, Y > y) = \left[ (1-u)^{-1/\gamma} + (1-v)^{-1/\gamma} - 1\right]^{-\gamma}
$

Where u = F(x) and v = F(y)