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Jones, M. C.
(2002).
DOI: https://doi.org/10.1198/000313002588
Abstract
It is well known that if X and Y are uniformly distributed over the region between the horizontal axis and a density function f, then X is distributed according to density f. The algorithm “generate Y from its marginal distribution, then X from its uniform conditional distribution given Y = y” follows. The main point made in this article is that for monotone and unimodal distributions, this construction reduces to Khintchine’s theorem, thereby yielding a simple explication thereof. This observation is followed up with further consideration of the general, nonunimodal, case for both univariate and multivariate distributions, and parallels are drawn with an alternative random variate generation method called vertical density representation.
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About
- Item ORO ID
- 22669
- Item Type
- Journal Item
- ISSN
- 0003-1305
- Keywords
- monotone density; uniform distribution; unimodal density; vertical density representation
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2002 American Statistical Association
- Depositing User
- Sarah Frain