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Visualizing the Probability Integral Transform

The probability integral transform is an important statement in statistics, used to generate random variables from a given continuous distribution by generating variables from the uniformly distribution on the interval [0,1]. Here, the principle is visualized by: generating random variables from a given distribution, evaluating the CDF at these samples, and plotting the histogram of these values. With increasing samples, it is clear that this distribution is uniform on [0,1].

Contributed by: Oliver K. Ernst

SNAPSHOTS

DETAILS

Snapshot 1-3: the convergence of the distribution to uniform on [0,1]. The random distribution generated is a mixture of Gaussians.