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The Probability Integral Transform and Related Results
John E. Angus
SIAM Review
Vol. 36, No. 4 (Dec., 1994), pp. 652-654
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2132726
Page Count: 3
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Abstract
A simple proof of the probability integral transform theorem in probability and statistics is given that depends only on probabilistic concepts and elementary properties of continuous functions. This proof yields the theorem in its fullest generality. A similar theorem that forms the basis for the inverse method of random number generation is also discussed and contrasted to the probability integral transform theorem. Typical applications are discussed. Despite their generality and far reaching consequences, these theorems are remarkable in their simplicity and ease of proof.
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SIAM Review © 1994 Society for Industrial and Applied Mathematics