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Journal Article

A Note on Bivariate Distributions That Are Conditionally Normal

Andrew Gelman and Xiao-Li Meng
The American Statistician
Vol. 45, No. 2 (May, 1991), pp. 125-126
DOI: 10.2307/2684374
Stable URL:
Page Count: 2

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Topics: Conditional probabilities, Statistical discrepancies
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It is possible for a nonnormal bivariate distribution to have conditional distribution functions that are normal in both directions. This article presents several examples, with graphs, including a counterintuitive bimodal joint density. The graphs simultaneously display the joint density and the conditional density functions, which appear as Gaussian curves in the three-dimensional plots.

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