I'm trying to find two statistics $T_1$, $T_2$ such that $(T_1, T_2)$ is jointly sufficient for $(\lambda, \theta)$ for a random sample $X_1, \dots, X_n$ from a two parameter exponential distribution.
$f(x) = \begin{cases} \lambda e^{-\lambda (x-\theta)}, & \theta < x < \infty, \\ 0, & \text{elsewhere}. \end{cases}$
Thanks.