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Math Help - Copula

  1. #1
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    May 2008
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    Copula

    Given two independent random variable X, Y such that

    <br />
F(x) = P(X \leq x) = 1-e^{-\gamma x},\ F(y) = P(Y \leq y)= 1-e^{-\gamma y}<br />

    how could be demonstrated through Copula with uniform distributions that

    <br />
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}<br />

    or, alternatively that

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

    Where u = F(x) and v = F(y)
    Last edited by dummyid; May 29th 2008 at 11:47 AM.
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