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Example: Exponential Deviates
Suppose we want p(y) dy = e-y dy, y [0,∞).
Apply the transformation method:
- Have f(y) = e-y, F(y) = e-0 -e-y = 1 -e-y.
- Set x = F(y)/F(∞) and solve x(1 -e-∞) = 1 -e-y for y.
- Get y(x) = -ln(1 -x).
So if x is a uniform deviate between 0 and 1, y(x) (x < 1) will be an exponential deviate.
See NRiC §7.2 for Gaussian deviates.