The Method
The problem that the inverse transform sampling method solves is as follows:
- Let X be a random variable whose distribution can be described by the cumulative distribution function F.
- We want to generate values of X which are distributed according to this distribution.
The inverse transform sampling method works as follows:
- Generate a random number u from the standard uniform distribution in the interval .
- Compute the value x such that F(x) = u.
- Take x to be the random number drawn from the distribution described by F.
Expressed differently, given a continuous uniform variable U in and an invertible cumulative distribution function F, the random variable X = F −1(U) has distribution F (or, X is distributed F).
A treatment of such inverse functions as objects satisfying differential equations can be given. Some such differential equations admit explicit power series solutions, despite their non-linearity.
Read more about this topic: Inverse Transform Sampling
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