Results of fitting simulated data with a constant and a Lorentzian QPO model. Each of the four panels shows the histogram of the estimates for one of the four model parameters (top left, a; bottom left, ν ₀; top right, w; bottom right, R). The parameters were estimated using the MLE (black line) and the min(χ ²) method (blue line) by fitting the average of M = 4 periodograms (4096 samples). For min(χ ²) fitting, outliers in the parameter distribution (e.g., fitted R ⩾ 100) were removed before building the histograms (about 2% of the total sample are outliers). The vertical dashed line indicates the true parameter values for the simulations. Clearly, the MLEs show no strong biases, but the min(χ ²) results underestimate both the Poisson level and the QPO amplitude. The estimates have generally larger spreads from min(χ ²) fitting than from the MLE.