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*): 37.6682
Mean of the chroma value (CIE L*a*b*): 16.7855
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 34.2308dB)

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: 0.4814
Contrast: 1.703
Low midtone range: 1.6858
High midtone range: 1.3742
Saturation: 0.67201
Frequencies: 0.777, 0.982, 1.028, 1.022, 1.044