Best-fitting PDE model in several redshift bins computed by integrating the XLF over redshift and column density. The purple shaded regions represent the 68% and 95% confidence intervals of the model, while the purple data points indicate the binned luminosity function. Our results are compared with the parametric forms of the XLF derived by previous X-ray studies (Ueda et al. 2014; Vito et al. 2014; Georgakakis et al. 2015; Peca et al. 2023) in the column density interval of log N_H = 20 − 24 (upper panels). Also shown is our XLF integrating over log N_H = 20 − 26 (lower panels) to the results of Buchner et al. (2015), Vito et al. (2018), Wolf et al. (2021), Barlow-Hall et al. (2023). The XLF of Buchner et al. (2015) in the first two panels are derived in the redshift range 3.2 ≤ z ≤ 4.0 and 4.0 ≤ z ≤ 7.0, respectively. Our PDE model at the last panel is extrapolated at z = 6.05. The brown dash-dotted lines show the predicted XLF derived by Ananna et al. (2019).