Definition
The probability integral transform states that if is a continuous random variable with cumulative distribution function, then the random variable has a uniform distribution on . The inverse probability integral transform is just the inverse of this: specifically, if has a uniform distribution on and if has a cumulative distribution, then the cumulative distribution function of the random variable is .
Read more about this topic: Inverse Transform Sampling
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—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
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