I have used a sample of long Gamma Ray Bursts ( GRBs ) common to both Swift and 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 \times 10 ^ { 52 } { 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 } \sim 0.3 \times 10 ^ { 52 } \left ( 1 + z \right ) ^ { 2.90 } { 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 AstroSat , as a function of redshift and luminosity . This demonstrates that via a quick localization and redshift measurement of even a few CZTI GRBs , AstroSat will help in improving the statistics of GRBs both typical and peculiar .