Original tone mapped image by DATMO {e=1, c=0.6}:

Histogram of the tone mapped image:

Image statistics of the tone-mapped image:

Median percentile of the lightness (CIE L*a*b*): 8.9203
Mean of the chroma value (CIE L*a*b*): 5.2683
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 39.1771dB)

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: 0.99255
Contrast: 0.80254
Low midtone range: 1.8289
High midtone range: 1.3414
Saturation: 0.22785
Frequencies: -0.159, 0.718, 1.003, 1.002, 1.005