  We investigate the statistics of photons emitted by tunneling electrons in a
single electronic level plasmonic nanojunction. We compute the waiting-time
distribution of successive emitted photons $w(\tau)$. When the cavity damping
rate $\kappa$ is larger than the electronic tunneling rate $\Gamma$, we show
that in the photon-antibunching regime, $w(\tau)$ indicates that the average
delay-time between two successive photon emission events is given by
$1/\Gamma$. This is in contrast with the usually considered second-order
correlation function of emitted photons, $g^{(2)}(\tau)$, which displays the
single time scale $1/\kappa$. Our analysis shows a relevant example for which
$w(\tau)$ gives independent information on the photon-emission statistics with
respect to $g^{(2)}(\tau)$, leading to a physical insight on the problem. We
discuss how this information can be extracted from experiments even in presence
of a non-perfect photon detection yield.
