Pixel histogram of the brightness temperature distribution and related lognormal fitting results. Upper left panel: histogram of the pixels of the brightness temperature distribution of the redshift-space mock map from 990 MHz to 1000 MHz smoothed by a 40 arcmin Gaussian kernel. After smoothing, the histogram can be very well fit by the lognormal distribution. The fitted parameters, s, loc, and scale, are shown as a function of the redshift (frequency) in the other three panels. For each of them we also fit a parabola function, which is a good fit. The lognormal fitted parameters are shown in red for the HOD mock and in blue for the HAM mock. Crosses represent the real-space mock and dots the redshift-space mock. The parabola fitting curves are shown in red for the HOD mock and in blue for the HAM mock. Solid lines show the real-space mock, and dashed lines show the redshift-space mock.