Luminosity Selection for Gamma Ray Bursts
  There exists an inevitable scatter in intrinsic luminosity of Gamma Ray
Bursts(GRBs). If there is relativistic beaming in the source, viewing angle
variation necessarily introduces variation in the intrinsic luminosity
function(ILF). Scatter in the ILF can cause a selection bias where distant
sources that are detected have a larger median luminosity than those detected
close by.
  Median luminosity, as we know, divides any given population into equal
halves. When the functional form of a distribution is unknown, it can be a more
robust diagnostic than any that use trial functional forms. In this work we
employ a statistical test based on median luminosity and apply it to test a
class of models for GRBs. We assume that the GRB jet has a finite opening angle
and that the orientation of the GRB jet is random relative to the observer. We
parameterize the jet with constant Lorentz factor $\Gamma$ and opening angle
$\theta_0$.
  We calculate $L_{median}$ as a function of redshift with an average of 17
grbs in each redshift bin($dz=0.01$) empirically, theoretically and use Fermi
GBM data, noting that SWIFT data is problematic as it is biased, specially at
high redshifts. We find that $L_{median}$ is close to $L_{max}$ for
sufficiently extended GRB jet and does not fit the data. We find an acceptable
fit with the data when $\Gamma$ is between $100$ and $200$, $\theta_0\leq 0.1$,
provided that the jet material along the line of sight to the on axis observer
is optically thick, such that the shielded maximum luminosity is well below the
bare $L_{max}$. If we associate an on-axis observer with a classically
projected monotonically decreasing afterglow, we find that their ILF is similar
to those of off-jet observer which we associate with flat phase afterglows.
