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We have used a technique based on analysis of normalized integral moments to test the compatibility of various Friedmann cosmological models (including those which admit a cosmological constant $\Lambda$) with the intensity distribution of gamma--ray bursts observed by BATSE. We find that models with a zero $\Lambda$ and a (typical) spectral index $\alpha$ = 2 are consistent with the data only if the maximum redshift observed by BATSE is less than 1.25. Higher limiting redshifts are possible only if the bursts have a spectrum much flatter than typically observed, or if they are embedded in a Universe with a positive $\Lambda$. Furthermore, the closer the actual value of the maximum redshift to the limiting values derived, the narrower must be the width of the luminosity distribution function for the bursts. Coupled with a similar result for Euclidean geometries (see the paper by Horack and Emslie elsewhere at this meeting), this result requires that if gamma--ray bursts truly span a wide range of burst luminosities, then they must not only be cosmological in origin, but also must be embedded in a Universe with a positive cosmological constant.
