  Many of the important conclusions about Gamma-Ray Bursts follow from the
distributions of various quantities such as peak flux or duration. We show that
for astrophysical transients such as bursts, multiple selection thresholds can
lead to various forms of data truncation, which can strongly affect the
distributions obtained from the data if not accounted for properly. Thus the
data should be considered to form a multivariate distribution. We also caution
that if the variables forming the multivariate distribution are not
statistically independent of each other, further biases can result. A general
method is described to properly account for these effects, and as a specific
example we extract the distributions of flux and duration from the BATSE 3B
Gamma-Ray Burst data. It is shown that properly accounting for the
aforementioned biases tends to increase the slope of the $\log{N}$-$\log{S}$
relation at low values of $S$, and dramatically increases the number of short
duration bursts.
