Calibration of Tests for Time Dilation in GRB Pulse Structures

Two tests for cosmological time dilation in $\gamma$-ray bursts -- the peak alignment and auto-correlation statistics -- involve averaging information near the times of peak intensity. Both tests require width corrections, assuming cosmological origin for bursts, since narrower temporal structure from higher energy would be redshifted into the band of observation, and since intervals between pulse structures are included in the averaging procedures. We analyze long ($>$ 2 s) BATSE bursts and estimate total width corrections for trial time-dilation factors (TDF = [1+$z_{\rm dim}$]/[1+$z_{\rm brt}$]) by time-dilating and redshifting bright bursts. Both tests reveal significant trends of increasing TDF with decreasing peak flux, but neither provides sufficient discriminatory power to distinguish between actual TDFs in the range 2--3.