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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—Ralph Waldo Emerson (1803–1882)
“Traditional scientific method has always been at the very best 20-20 hindsight. It’s good for seeing where you’ve been. It’s good for testing the truth of what you think you know, but it can’t tell you where you ought to go.”
—Robert M. Pirsig (b. 1928)