A few months ago I wrote a computer simulation to analyse common noise variability for a number of distributions. Firstly, I chose the ideal observers I was interested in and determined their signal+noise and noise-alone distributions. I chose: Normal-Normal with equal variance and different means, Rayleigh-Rayleigh for given signal-to-noise ratios, and Uniform-Uniform equal variance and different means. At the beginning of each simulation, I chose one ideal observer with one set of parameters.

I calculated the theoretical ROC curve and area. Then I took samples of size N are from the signal+noise and noise-alone distributions. This resulted in N samples that were independently and identically distributed for each event. This involved generating random numbers and converting them to Rayleigh, Normal, or Uniform variates.