  Based on the standard energy reservoir of gamma-ray burst (GRB) jets and the
relationship between peak energy ($E_p$) of $\nu F_{\nu}$ spectrum and the
equivalent-isotropic energy ($E_{\rm{iso}}$), we test the GRB probability
distributions as a function of viewing angle ($\theta$) and of viewing angle
together with redshift $z$, $P(\theta)$ and $P(\theta,z)$, predicted by the
universal-structured jet (USJ) model with simulations on observational bases
for a detection threshold of $S>4 \times 10^{-5}$ erg cm$^{-2}$, where $S$ is
the total fluence in an energy band $>20$ keV. We simulate a sample including
$10^{6}$ GRBs, and then derive $P(\theta)$ and $P(\theta,z)$. We show that both
simulated and theoretical $P(\theta)$ and $P(\theta,z)$ are consistent with
each other. This consistency seems to be regarded as support for the USJ model.
A small difference between the theoretical and simulated results might be due
to the observed $E_p$ distribution used in our simulations, which perhaps
suffers a little of biases for $E_p<100$ keV.
