Table 6 PMF of bivariate binary variables using Gaussian copula

(Y₁,Y₂)

(0, 0)

C(q₁,q₂; γ₁₂)=Φ₂(Φ⁻¹(0.2),Φ⁻¹(0.3);0.752)=0.1517

(0, 1)

q₁−C(q₁,q₂; γ₁₂)=0.2−0.1517=0.0483

(1, 0)

q₂−C(q₁,q₂; γ₁₂)=0.3−0.1517=0.1483

(1, 1)

1−q₁−q₂+C(q₁,q₂; γ₁₂)=1−0.2−0.3+0.1517=0.6517

(Y₂,Y₃)

(0, 0)

C(q₂,q₃; γ₂₃)=Φ₂(Φ⁻¹(0.3),Φ⁻¹(0.4);0.607)=0.2097

(0, 1)

q₂−C(q₂,q₃; γ₂₃)=0.3−0.2097=0.0903

(1, 0)

q₃−C(q₂,q₃; γ₂₃)=0.4−0.2097=0.1903

(1, 1)

1−q₂−q₃+C(q₂,q₃; γ₂₃)=1−0.3−0.4+0.2097=0.5097