  We use the BD2 sample of gamma-ray bursts (GRBs) based on 5.9 years of BATSE
DISCLA data with a variety of models of the luminosity function to derive
characteristic GRB luminosities, space densities and redshift distributions.
Previously published results for an open universe and modest density evolution
of the GRBs showed characteristic peak luminosities around 5x10**51 erg/s in
the 50-300 keV band if the emission is isotropic, and local space densities
around 0.2 Gpc**-3 yr**-1. In this paper, we illustrate for several luminosity
function models the predicted distributions of peak flux, luminosity and
redshifts. We use the luminosity function models also to address the connection
between supernovae and GRB. If all supernovae of Type Ib/c harbor a GRB, the
beaming fraction would have to be 10**-5 - 10**-3.5. We find that GRB 980425,
if correctly identified with SN 1998bw, has to be part of a population
different from that of the bulk of GRBs.
