Density Estimation of the <scp>GRBs'</scp> Redshift Distribution and Its Connection to Cosmic Star Formation History

ABSTRACT We analyze the Gamma‐Ray Burst (GRB) redshift distribution using various density estimation methods. Several density estimators for one‐dimensional point processes were tested for different sample sizes up to 1200 events. Our goal was to identify the “best” non‐parametric radial density estimator for GRBs, and we found that Poisson noise significantly influences results. We identified Boundary Corrected Kernel Density Estimation as the most suitable method and applied it to a dataset of 542 GRBs with spectroscopic redshifts and reconstructed the GRB density function for different distances/redshifts. The relationship between the observed GRB redshift distribution and the cosmic star formation history is briefly discussed.