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We present a catalog of the redshift estimates and probability distributionsfor 1366 individual Long-duration Gamma-Ray Bursts (LGRBs) detected by theBurst And Transient Source Experiment (BATSE). This result is based on acareful classification and modeling of the population distribution of BATSELGRBs in the 5-dimensional space of redshift as well as intrinsic promptgamma-ray emission properties: peak luminosity, total isotropic emission, thespectral peak energy, and the intrinsic duration, while taking into account thedetection mechanism of BATSE and sample incompleteness. The underlyingassumption in our modeling approach is that LGRBs trace the Cosmic StarFormation Rate and that the joint 4-dimensional distribution of theaforementioned prompt gamma-ray emission properties follows a multivariatelog-normal distribution. Our modeling approach enables us to constrain theredshifts of BATSE LGRBs to average uncertainty ranges of $0.7$ and $1.7$ at$50\%$ and $90\%$ confidence levels, respectively. Our predictions are almostentirely at odds with the previous estimates of BATSE redshifts based on thephenomenological high-energy correlations, in particular with the estimatesderived from the lag-luminosity and the variability-luminosity relations. Thereis, however, a weak but significant correlation of strength $\sim0.26$ betweenour predicted redshift estimates and those derived from the hardness-brightnessrelations. The discrepancies between the estimates can be explained by thestrong influence of sample incompleteness in shaping the phenomenologicallyproposed high-energy correlations in the literature. The presented catalog herecan be useful for demographic studies of LGRBs and studies of individual BATSEevents.

A Catalog of Redshift Estimates for 1366 BATSE Long-Duration Gamma-Ray  Bursts: Evidence for Strong Selection Effects on the Phenomenological Prompt  Gamma-Ray Correlations