Assume we have two random variables $X_1\sim Exp(2)$, $X_2\sim Exp(1/2)$. I need to find a joint distribution function, so that Kendall's Tau will be $\rho_\tau(X_1,X_2)=-0.85$. I know that somehow I need to use a theorem: $\rho_\tau(X_1,X_2)=4\int_0^1\int_0^1(C(u_1,u_2)-1)dC(u_1,u_2)$, where $C$ is the Copula, but sadly I don't have any idea how I can exactly find a joint cdf.
2026-02-23 12:44:59.1771850699
Find a joint distribution function with known Kendall's tau (Copula)
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