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The source counts or the so-called log N -- log S relations are the primary data that constrain the spatial distribution of sources with unknown distances, such as gamma-ray bursts. In order to test galactic, halo, and cosmological models for gamma-ray bursts we compare theoretical characteristics of the log N -- log S relations to those obtained from data gathered by the BATSE instrument on board the Compton Observatory (GRO) and other instruments. We use a new and statistically correct method, that takes proper account of the variable nature of the triggering threshold, to analyze the data. Constraints on models obtained by this comparison will be presented. This work is supported by NASA grants NAGW 2290, NAG5 2036, and NAG5 1578.
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