Time Dilation of BATSE $\gamma$-ray Bursts

We perform several nonparametric correlation tests on the BATSE 3B data to search for evidence of cosmological time dilation. These tests account for the effects of data truncation due to threshold effects in both limiting brightness and limiting duration, enabling us to utilize a larger number of bursts than in previous analyses. We find little significant evidence for correlation between various measures of peak intensity and duration, but the tests cannot conclusively rule out time dilation factors of 2 or less without more data. There is stronger evidence for a positive correlation between fluence and duration, which if confirmed would rule out simple no-evolution cosmological models unless there is a strong intrinsic correlation between the total radiant energy and the duration of bursts