  We present a theoretical and experimental study aimed at characterizing
statistical regimes in a random laser. Both the theoretical simulations and the
experimental results show the possibility of three region of fluctuations
increasing the pumping energy. An initial Gaussian regime is followed by a
L\'evy statistics and Gaussian statistic is recovered again for high pump pulse
energy. These different statistical regimes are possible in a weakly diffusive
active medium, while the region of L\'evy statistics disappears when the medium
is strongly diffusive presenting always a Gaussian regime with smooth emission
spectrum. Experiments and theory agree in identification of the key parameters
determining the statistical regimes of the random laser.
