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.

Read more about this topic:  Inverse Transform Sampling

Famous quotes containing the word method:

    A method of child-rearing is not—or should not be—a whim, a fashion or a shibboleth. It should derive from an understanding of the developing child, of his physical and mental equipment at any given stage, and, therefore, his readiness at any given stage to adapt, to learn, to regulate his behavior according to parental expectations.
    Selma H. Fraiberg (20th century)

    The method of authority will always govern the mass of mankind; and those who wield the various forms of organized force in the state will never be convinced that dangerous reasoning ought not to be suppressed in some way.
    Charles Sanders Peirce (1839–1914)