  We show that the Euclidean value of <V/Vmax> for gamma-ray bursts (GRB)
selected on a timescale of 1024 ms is correlated with spectral hardness. The
value of <V/Vmax> ranges from 0.42 for soft bursts to 0.26 for the hardest
bursts. Given that the Euclidean value of <V/Vmax> 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 cannot be shown explicitly due to the
small number of observed GRB redshifts at the present time. Based on the
<V/Vmax>-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 around 10^51.5 erg s^-1 in the 50-300
keV range and total local rate densities of 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 about 20
times more luminous than the softest ones.
