  The distribution of the apparent total energy emitted by a gamma-ray burst
reflects not only the distribution of the energy actually released by the burst
engine, but also the distribution of beaming angles. Using the observed energy
fluences, the detection thresholds and burst redshifts for three burst samples,
I calculate the best-fit parameters for lognormal and power-law distributions
of the apparent total energy. Two of the samples include a small number of
bursts with spectroscopic redshifts, while the third sample has 220 bursts with
redshifts determined by the proposed variability-luminosity correlation. I find
different sets of parameter values for the three burst samples. The Bayesian
odds ratio cannot distinguish between the two model distribution functions for
the two smaller burst samples with spectroscopic redshifts, but does favor the
lognormal distribution for the larger sample with variability-derived
redshifts. The data do not rule out a distribution with a low energy tail which
is currently unobservable. I find that neglecting the burst detection threshold
biases the fitted distribution to be narrower with a higher average value than
the true distribution; this demonstrates the importance of determining and
reporting the effective detection threshold for bursts in a sample.
