Original tone mapped image by Camera {x=big, c=1.8}:

Histogram of the tone mapped image:

Image statistics of the tone-mapped image:

Median percentile of the lightness (CIE L*a*b*): 24.1016
Mean of the chroma value (CIE L*a*b*): 6.3573
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 33.5589dB)

Fitted tone curve of the generic tone mapping operator,
compared to the luminance compression done by the tone mapping operator:

Fitted parameters of the generic tmo:

Exposure: 3.694
Contrast: 1.6599
Low midtone range: 1.5616
High midtone range: 1.1222
Saturation: 0.49838
Frequencies: -0.077, 0.794, 0.994, 1.004, 1.03