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1

Note that the survival copula $C_{\theta_A, \theta_B}(u, v)$ and the non-survival copula $C(u, v)$ are related by \begin{align*} C_{\theta_A, \theta_B}(\hat{u}, \hat{v}) = \hat{u}+\hat{v}-1 + C(1-\hat{u}, 1-\hat{v}), \end{align*} where $\hat{u}=\bar{F}_A(x)=1 - F_A(x)$ and $\hat{v}=\bar{F}_B(y)=1-F_B(y)$. Then, \begin{align*} C(u, v) = C_{\theta_A, \theta_B}(...


2

$$\text{Pr}[\tau_1>t,\tau_2\leq t,\tau_3\leq t]=\text{Pr}[\tau_2\leq t,\tau_3\leq t] - \text{Pr}[\tau_1\leq t,\tau_2\leq t,\tau_3\leq t]$$ $$\text{Pr}[\tau_2\leq t,\tau_3\leq t]=C(1,q_2(t),q_3(t))$$



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