  We present a catalog of the redshift estimates and probability distributions
for 1366 individual Long-duration Gamma-Ray Bursts (LGRBs) detected by the
Burst And Transient Source Experiment (BATSE). This result is based on a
careful classification and modeling of the population distribution of BATSE
LGRBs in the 5-dimensional space of redshift as well as intrinsic prompt
gamma-ray emission properties: peak luminosity, total isotropic emission, the
spectral peak energy, and the intrinsic duration, while taking into account the
detection mechanism of BATSE and sample incompleteness. The underlying
assumption in our modeling approach is that LGRBs trace the Cosmic Star
Formation Rate and that the joint 4-dimensional distribution of the
aforementioned prompt gamma-ray emission properties follows a multivariate
log-normal distribution. Our modeling approach enables us to constrain the
redshifts of BATSE LGRBs to average uncertainty ranges of $0.7$ and $1.7$ at
$50\%$ and $90\%$ confidence levels, respectively. Our predictions are almost
entirely at odds with the previous estimates of BATSE redshifts based on the
phenomenological high-energy correlations, in particular with the estimates
derived from the lag-luminosity and the variability-luminosity relations. There
is, however, a weak but significant correlation of strength $\sim0.26$ between
our predicted redshift estimates and those derived from the hardness-brightness
relations. The discrepancies between the estimates can be explained by the
strong influence of sample incompleteness in shaping the phenomenologically
proposed high-energy correlations in the literature. The presented catalog here
can be useful for demographic studies of LGRBs and studies of individual BATSE
events.
