Comparison of real Cyg X-1 hard state data (blue circles) with simulated data showing the same power spectrum, made using the K16 model (green triangles) or the “exponentiated” model of UMV05 (open red squares). Top left: power spectra of the light curves, including the best-fitting Lorentzian decomposition for the real data (black lines, total model line in solid red). Top right: flux distributions (flux normalised by mean count rate), models (coloured lines) and data/model ratios for a fit to a lognormal model with constant offset constrained to be non-negative. Bottom panels: the rms-flux relations of the light curves obtained for rms measured on two different time-scale ranges, short (0.125−1 s, bottom left panel) and long (4−32 s, bottom right panel). Best-fitting linear (plus constant) relations are also shown as dotted lines. For the flux distributions and rms-flux relations, the K16 model is strongly inconsistent with the data, while the UMV05 model works reasonably well.