We show that the Euclidean value of < V / V _ { max } > for gamma-ray bursts ( GRB ) selected on a timescale of 1024 ms is correlated with spectral hardness .
The value of < V / V _ { max } > ranges from \sim 0.42 for soft bursts to \sim 0.26 for the hardest bursts .
Given that the Euclidean value of < V / V _ { max } > for cosmological objects in a well defined sample is a distance indicator , the hard bursts must reside at larger redshifts and therefore be more luminous than the soft bursts .
The resulting luminosity-hardness correlation can not be shown explicitly due to the small number of observed GRB redshifts at the present time .
Based on the < V / V _ { max } > -hardness correlation , we derive the luminosity function of GRBs without using any redshifts , but we have to make an assumption how the comoving GRB rate varies with redshift .
We present luminosity functions for three models of the GRB rate as a function of redshift , based on star formation rates .
The peak luminosity functions are approximately broken power laws with an isotropic-equivalent break luminosity of \sim 10 ^ { 51.5 } erg s ^ { -1 } in the 50 - 300 keV range and total local rate densities of \sim 0.5 Gpc ^ { -3 } y ^ { -1 } .
Predicted GRB counts as a function of flux and redshift are presented .
Based on the GRB luminosity function , we carry out a simulation to produce the luminosity-hardness correlation , which shows that the hardest GRBs are \sim 20 times more luminous than the softest ones .