Original tone mapped image by PTMO {g=1.6, 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*): 26.1642
Mean of the chroma value (CIE L*a*b*): 36.4716
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 27.5dB)

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: 2.4644
Contrast: 1.2221
Low midtone range: 1.4851
High midtone range: 1.6
Saturation: 0.8616
Frequencies: -0.036, 0.7, 1.32, 1.173, 1.174