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*): 9.1732
Mean of the chroma value (CIE L*a*b*): 13.9197
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 28.0208dB)

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: 0.53285
Contrast: 1.6957
Low midtone range: 1.5278
High midtone range: 4.3812
Saturation: 0.48404
Frequencies: -0.142, 0.774, 1.044, 1.012, 1.01