  Le & Dermer developed a gamma-ray burst (GRB) model to fit the redshift and
the jet opening angle distributions measured with pre-Swift and Swift missions
and showed that GRBs do not follow the star formation rate. Their fitted
results were obtained without the opening angle distribution from Swift with an
incomplete Swift sample, and that the calculated jet opening angle distribution
was obtained by assuming a flat $\nu F_\nu$ spectrum. In this paper, we revisit
the work done by Le & Dermer with an assumed broken power law GRB spectrum.
Utilizing more than 100 GRBs in the Swift sample that include both the observed
estimated redshifts and jet opening angles, we obtain a GRB burst rate
functional form that gives acceptable fits to the pre-Swift and Swift redshift
and jet opening angle distributions with an indication that an excess of GRBs
exists at low redshift below $z \approx 2$. The mean redshifts and jet opening
angles for pre-Swift~(Swift) are $\langle z \rangle \sim 1.3$ ($1.7$) and
$\langle \theta_{\rm j} \rangle \sim 7^o$ ($11^o$), respectively. Assuming a
GRB rate density (SFR9), similar to the Hopkins & Beacom star formation history
and as extended by Li, the fraction of high-redshift GRBs is estimated to be
below 10% and 5% at $z \geq 4$ and $z\geq 5$, respectively, and below 10% at $z
\leq 1$.
