IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
If U is Uniform(0,1) and F is a continuous, strictly increasing distribution function, which statement about the inverse transform method is correct?
F inverse of U has distribution function F. This is because the probability that F^(-1)(U) is at most x equals the probability that U is at most F(x), which is F(x) since U is uniform on (0,1).
- AF^(-1)(U) has distribution function FCorrect
- BF(U) has distribution function F
- CF^(-1)(U) is Uniform(0,1)
- D1 - F(U) has distribution function F
- F^(-1)(U) has the same distribution as U only when F is normal
Explanation
P(F^(-1)(U) <= x) = P(U <= F(x)) = F(x), so F^(-1)(U) has distribution F. The reverse transform F(X) is uniform, not F(U) distributed as F.
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