  A statistical analysis of the laser excitation of cold and randomly
distributed atoms to Rydberg states is developed. We first demonstrate with a
hard ball model that the distribution of energy level shifts in an interacting
gas obeys L\'evy statistics, in any dimension $d$ and for any interaction
$-C_p/R^p$ under the condition $d/p<1$. This result is confirmed with a Monte
Carlo rate equations simulation of the actual laser excitation in the
particular case $p=6$ and $d=3$. With this finding, we develop a statistical
approach for the modeling of probe light transmission through a cold atom gas
driven under conditions of electromagnetically induced transparency involving a
Rydberg state. The simulated results are in good agreement with experiment.
