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*): 90.9075
Mean of the chroma value (CIE L*a*b*): 11.2603
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 32.7807dB)

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: 3.4695
Contrast: 1.6743
Low midtone range: 1.4925
High midtone range: 1.1164
Saturation: 0.54044
Frequencies: -0.12, 0.744, 0.966, 0.969, 0.989