  We use the lag-luminosity relation to calculate self-consistently the
redshifts, apparent peak bolometric luminosities L_B, and isotropic energies
E_iso for a large sample of BATSE gamma-ray bursts. We consider two different
forms of the lag-luminosity relation; for both forms the median redshift for
our burst database is 1.6. We model the resulting E_iso sample with power law
and Gaussian probability distributions without redshift evolution, both of
which are reasonable models. The power law model has an index of
alpha_E=1.76+/-0.05 (95% confidence), where p(E_iso) propto E_iso^(-alpha_E).
The simple universal jet profile model suggested but did not require alpha_E=2,
and subsequent physically reasonable refinements to this model permit greater
diversity in alpha_E, as well as deviations from a power law; therefore our
observed E_iso probability distribution does not disprove the universal jet
model.
