  Gamma-ray bursts are believed to be some catastrophic event in which material
is ejected at a relativistic velocity, and internal collisions within this
ejecta produce the observed $\gamma$-ray flash. The angular size of a causally
connected region within a relativistic flow is of the order the angular width
of the relativistic beaming, $\gamma^{-1}$. Thus, different observers along
different lines of sights could see drastically different fluxes from the same
burst. Specifically, we propose that the most energetic bursts correspond to
exceptionally bright spots along the line of sight on colliding shells, and do
not represent much larger energy release in the explosion. We calculate the
distribution function of the observed fluence for random angular-fluctuation of
ejecta. We find that the width of the distribution function for the observed
fluence is about two orders of magnitude if the number of shells ejected along
different lines of sight is ten or less. The distribution function becomes
narrower if number of shells along typical lines of sight increases. The
analysis of the $\gamma$-ray fluence and afterglow emissions for GRBs with
known redshifts provides support for our model i.e. the large width of GRB
luminosity function is not due to a large spread in the energy release but
instead is due to large angular fluctuations in ejected material. We outline
several observational tests of this model. In particular, we predict little
correlation between the $\gamma$-ray fluence and the afterglow emission as in
fact is observed. We predict that the early (minutes to hours) afterglow would
depict large temporal fluctuations whose amplitude decreases with time. Finally
we predict that there should be many weak bursts with about average afterglow
luminosity in this scenario.
