Abstract
The aim of the present work is to estimate the rate and luminosity functions of short, intermediate and long gamma-ray bursts (GRBs) by fitting their intensity distributions with parameterized explosion rates and luminosity functions. The results show that the parameters of the rate and luminosity function for long GRBs can be calculated with an accuracy of 10–30%. However, some parameters of intermediate and short GRBs have large uncertainties. An important conclusion is that there was initially a large outburst in the frequency of long GRBs, and consequently a large outburst in the star-formation rate, if they come from collapsars. Finally, a simulated intensity distribution has been constructed to test the ability of the method to recover the simulated parameters.
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