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Aug 19 at 20:32 comment added whuber In the common case where $\epsilon = 0.05\approx \exp(-3)$ and approximating $\log(1-\alpha)\approx\alpha,$ you have rediscovered the Rule of Three. There's no need to vary the distributions unless you're interested in exploring the effects of ties; the Probability Integral Transform for absolutely continuous variables permits you to assume the distribution is uniform.
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S Aug 19 at 9:18 history answered PedanticPete CC BY-SA 4.0