  We calculate the R\'enyi entropy of a positive integer order $M$ for a
reduced density matrix of a single-level quantum dot connected to left and
right leads. We exploit a $2 \times 2$ modified Keldysh Green function matrix
obtained by the discrete Fourier transform of a $2 M \times 2M$ multi-contour
Keldysh Green function matrix. A moment generating function of self-information
is deduced from the analytic continuation of $M$ to the complex plane. We
calculate the probability distribution of self-information and find that,
within the Hartree approximation, the on-site Coulomb interaction affects rare
events and modifies a bound of the probability distribution. A simple equality,
from which an upper bound of the average, i.e., the entanglement entropy, would
be inferred, is presented. For noninteracting electrons, the entanglement
entropy is expressed with current cumulants of the full-counting statistics of
electron transport.
