Original tone mapped image by iCAM06 {p=134, ct=0.8}:

Histogram of the tone mapped image:

Image statistics of the tone-mapped image:

Median percentile of the lightness (CIE L*a*b*): 53.308
Mean of the chroma value (CIE L*a*b*): 6.2691
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 22.798dB)

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: 0.13
Contrast: 1.3742
Low midtone range: 4.8203
High midtone range: 53.2446
Saturation: 0.20002
Frequencies: 1.046, 0.979, 0.977, 0.976, 0.956