  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 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 calculate
$L_{median}$ as a function of redshift by simulating GRBs empirically,
theoretically and use the luminosity vs redshift {\it Swift} data in order to
compare the theoretical results with the observed ones.
  The method accounts for the fact that at some redshifts there may be some
GRBs that go undetected. We find that $L_{median}$ is extremely insensitive to
the on-axis (i.e. maximal) luminosity of the jet.
