Assuming that the observed gamma-ray burst (GRB) rate as a function of redshift is proportional to a corrected star formation rate, we derive the empirical distribution of the viewing angles of long BATSE GRBs, $P^{rm em}(theta)$, and the distribution of these bursts in the plane of $theta$ against redshift, $P^{rm em}(theta, z)$, by using a tight correlation between $E_{gamma}$) and $E_{rm p}^{}$). Our results show that $P^{rm em}(theta)$ is well fitted by a log-normal distribution centering at $log theta/{rm rad}=-0.76$ with a width of $sigma_{log theta}=0.57$. We test different universal structured jet models by comparing model predictions with our empirical results. To make the comparisons reasonable, an effective threshold, which corresponds to the sample selection criteria of the long GRB sample, is used. We find that the predictions of a two-Gaussian jet model are roughly consistent with our empirical results. A brief discussion shows that cosmological effect on the $E_{gamma}-E_{rm p}^{}$ relation does not significantly affect our results, but sample selection effects on this relationship might significantly influence our results.
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