  We argue that the distributions of both the intrinsic fluence and the
intrinsic duration of the gamma-ray emission in gamma-ray bursts from the BATSE
sample are well represented by log-normal distributions, in which the intrinsic
dispersion is much larger than the cosmological time dilatation and redshift
effects. We perform separate bivariate log-normal distribution fits to the
BATSE short and long burst samples. The bivariate log-normal behavior results
in an ellipsoidal distribution, whose major axis determines an overall
statistical relation between the fluence and the duration. We show that this
fit provides evidence for a power-law dependence between the fluence and the
duration, with a statistically significant different index for the long and
short groups. We discuss possible biases which might affect this result, and
argue that the effect is probably real. This may provide a potentially useful
constraint for models of long and short bursts.
