Left panels: cumulative LGRB density distribution for the raw (blue) and corrected (orange) cases. The black solid line corresponds to the piecewise functional fit used to calculate the LGRB-RD later. Right panels: log–log distribution of Φ(L) and L (erg s⁻¹). The blue and orange open stars show the raw and corrected Φ ( > L) points, respectively. The black dashed lines correspond to the best-fit functions described in Equation (11). Residuals for raw and corrected σ (z), and raw and corrected Φ (>L) cases are shown in the bottom panel.