Exchangeable random variables: Difference between revisions

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Revision as of 16:36, 24 June 2007

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Let <math>\xi=\{E_1,\ldots,E_n\}</math> be a family of random events, and let <math>X_1,\ldots,X_n</math> be the [[indicator function]]s of the events in <math>\xi</math>. Then <math>\xi</math> is said to be '''exchangeable''' if, for any [[permutation]]

<math>j_1,\ldots,j_n</math> of the indexesindices <math>1,\ldots,n</math>, the two random vectors <math>(X_1,\ldots,X_n)</math> and <math>(X_{j_1},\ldots, X_{j_n})</math> have the same [[joint distribution]].

With a more general view, a family of generic random variables <math>(X_1,\ldots,X_n)</math> is exchangeable if, for any permutation <math>j_1\ldots,j_n</math> of the indexes <math>1,\ldots,n</math>, they have the same joint distribution.

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== References ==

* Spizzichino, Fabio ''Subjective probability models for lifetimes''. Monographs on Statistics and Applied Probability, 91. ''Chapman & Hall/CRC'', Boca Raton, FL, 2001. xx+248 pp. ISBN 1-58488-060-0

[[Category:Probability theory]]