Given a non-homogeneous Poisson process where $X_1$, $X_2$ is the time of first and second point and let $T_1$, $T_2$ ... be the interpoint distances. That is, $T_1 = X_1$, $T_2 = X_2-X_1$.
Also, $T_1$, $T_2$ are dependent and they have different distribution.
How should I find the joint distribution of ($T_1$, $T_2$) and ($X_1$, $X_2$)?