GRB Variability-Luminosity Correlation Confirmed

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Recently, Guidorzi et al. (2005) expanded the size of the sample of GRBs for which variabilities and peak luminosities have been measured, from 11 to 32. They confirm the existence of a correlation, but find a dramatically different relationship between L and V than had originally been found. We find that this is the result of improper statistical methodology. When we fit a model to the data that accommodates both statistical variance (in two dimensions) and sample variance, we find that L V³.4(+0.9,-0.6) with a sample variance of sigmaₗogV = 0.20(+0.04,-0.04), which is consistent with the original finding of Reichart et al. (2001) -- L V³.3(+1.1,-0.9) with a sample variance of sigmaₗogV = 0.18(+0.07,-0.05) -- and inconsistent with the finding of Guidorzi et al. (2005): L V¹.3(+0.8,-0.4) with sample variance assumed to be zero.