Selected CHIME FRB sample

The Lynden-Bell's c^-^ method is applied to study their energy function and event rate evolution with redshift (z). Using the non-parametric Kendell's {tau} statistics, it is found that the FRB energy (E) strongly evolves with redshift as E(z){prop.to}(1+z)^1.24^ for Sample 1, E(z){prop.to}(1+z)^0.98^ for Sample 2 and E(z){prop.to}(1+z)^1.99^ for Sample 3.

After removing the redshift dependence, the local energy distributions of the three samples can be well described by a broken power-law form with a broken energy of ~10^40^ erg. Meanwhile, the redshift distributions of Samples 1 and 2 are identical but different from that of Sample 3. Interestingly, we find that the event rates of Samples 1 and 2 of are independent of redshift, and Sample 3 decreases as a single power-law form with an index of -2.41.