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
Famous quotes containing the word method:
“Women stand related to beautiful nature around us, and the enamoured youth mixes their form with moon and stars, with woods and waters, and the pomp of summer. They heal us of awkwardness by their words and looks. We observe their intellectual influence on the most serious student. They refine and clear his mind: teach him to put a pleasing method into what is dry and difficult.”
—Ralph Waldo Emerson (1803–1882)
“The method of painting is the natural growth out of a need. I want to express my feelings rather than illustrate them. Technique is just a means of arriving at a statement.... I can control the flow of paint: there is no accident, just as there is no beginning and no end.”
—Jackson Pollock (1912–1956)