  We study the energy distribution function $\rho (E)$ for interfaces in a
random field environment at zero temperature by summing the leading terms in
the perturbation expansion of $\rho (E)$ in powers of the disorder strength,
and by taking into account the non perturbational effects of the disorder using
the functional renormalization group. We have found that the average and the
variance of the energy for one-dimensional interface of length $L$ behave as,
$<E>_{R}\propto L\ln L$, $\Delta E_{R}\propto L$, while the distribution
function of the energy tends for large $L$ to the Gumbel distribution of the
extreme value statistics.
