ML estimation for bivariate data.

Question

Consider the random variables $X$ and $Y$ with joint distribution $$F(x,y)=[1-e^{-a_{1}x}]^{\theta}+[1-e^{-a_{2}y}]^{\theta}-[1-e^{-a_{1}x-a_{2}y}]^{\theta},$$ where $a_{1}>0$, $a_{2}>0$, $0<\theta\leq 1$ and $x, y>0$. Clearly, when $\theta=1$, the random variables $X$ and $Y$ are independent. I am estimating the parameters $a_{1}$, $a_{2}$ and $\theta$, using a bivariate real data which has correlation coefficient .90. The MLE corresponding this data for $\theta$ is turns out to be around $.98000$, which implies the data nearly independent. Is this MLE for $\theta$ correct?