then 1 out of $\sim$40 low metallicity Ic-bl SNe give rise to an LGRB.

Using the process described above, we derive an expected LGRB event rate as follows: Beginning with the cosmic star-formation rate history of [@hb] and the [@form_rate_letter] estimates of the metallicity distribution of the universe as a function of redshift we obtain an estimate of the amount of star-formation above and below the [@diff_rate_letter] metallicity cutoff. The expected number of LGRBs formed is thus estimated after applying the [@diff_rate_letter] estimate of the effect of metallicity on the LGRB formulation rate per unit of available star-formation. The result is an expected LGRB event rate as a function of redshift which can then be scaled in the same manner as the observed LGRB populations described previously.

![\[redshift\_distribution\] The redshift distribution of various LGRB samples scaled as labeled such that the distributions are approximately 60 at redshift 2.5 which provides reasonable agreement across the lower redshift range. The purpose of this plot is to compare the redshift distributions of different LGRB samples and find any discrepancies beyond that different samples have a different total number of objects. Note that the @stats_paper (GF13) sample (thick black line in the inset plot) 