Exchangeable random variables: Difference between revisions

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Properties: cannot be extended
also sometimes '''interchangeable''', add ref
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An '''exchangeable sequence of random variables''' (also sometimes '''interchangeable''') is a
sequence ''X''<sub>1</sub>,&nbsp;''X''<sub>2</sub>,&nbsp;''X''<sub>3</sub>,&nbsp;... of [[random variable]]s such that for any finite [[permutation]] &sigma; of the indices 1, 2, 3, ..., i.e. any permutation &sigma; that leaves all but finitely many indices fixed, the [[joint probability distribution]] of the permuted sequence
 
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* Aldous, David J., ''Exchangeability and related topics'', in: École d'Été de Probabilités de Saint-Flour XIII — 1983, Lecture Notes in Math. 1117, pp. 1-198, Springer, Berlin, 1985. ISBN 978-3-540-15203-3 [http://dx.doi.org/10.1007/BFb0099421 DOI 10.1007/BFb0099421]
* Chow, Yuan Shih and Teicher, Henry, ''Probability theory. Independence, interchangeability, martingales,'' Springer Texts in Statistics, 3rd ed., Springer, New York, 1997. xxii+488 pp. ISBN 0-387-98228-0
* 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