  I have used a sample of long Gamma Ray Bursts (GRBs) common to both
\emph{Swift} and \emph{Fermi} to re-derive the parameters of the Yonetoku
correlation. This allowed me to self-consistently estimate pseudo redshifts of
all the bursts with unknown redshifts. This is the first time such a large
sample of GRBs from these two instruments are used, both individually and in
conjunction, to model the long GRB luminosity function. The GRB formation rate
is modelled as the product of the cosmic star formation rate and a GRB
formation efficiency for a given stellar mass. An exponential cut-off powerlaw
luminosity function fits the data reasonably well, with $\nu = 0.6$ and $ L_b =
5.4 \times10^{52} \, \rm{erg.s^{-1}},$ and does not require a cosmological
evolution. In the case of a broken powerlaw, it is required to incorporate a
sharp evolution of the break given by
$L_{b}\sim0.3\times10^{52}\left(1+z\right)^{2.90} \, \rm{erg.s^{-1}},$ and the
GRB formation efficiency (degenerate up to a beaming factor of GRBs) decreases
with redshift as $\propto\left(1+z\right)^{-0.80}.$ However it is not possible
to distinguish between the two models. The derived models are then used as
templates to predict the distribution of GRBs detectable by CZTI on board
\emph{AstroSat}, as a function of redshift and luminosity. This demonstrates
that via a quick localization and redshift measurement of even a few CZTI GRBs,
\emph{AstroSat} will help in improving the statistics of GRBs both typical and
peculiar.
