Inverse Transform Sampling - The Method

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:

1. Generate a random number u from the standard uniform distribution in the interval .
2. Compute the value x such that F(x) = u.
3. 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.