  We discuss the passage-time statistics of superradiant light pulses generated
during the scattering of laser light from an elongated atomic Bose-Einstein
condensate. Focusing on the early-stage of the phenomenon, we analyze the
corresponding probability distributions and their scaling behaviour with
respect to the threshold photon number and the coupling strength. With respect
to these parameters, we find quantities which only vary significantly during
the transition between the Kapitza Dirac and the Bragg regimes. A possible
connection of the present observations to Brownian motion is also discussed.
