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De Finetti's-type results for some families of non identically distributed random variables
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Ricardo Vélez Ibarrola, Statistics Department. UNED, Madrid, Spain
Tomás Prieto-Rumeau, Statistics Department. UNED, Madrid, Spain
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Abstract
We consider random selection processes of weighted elements in an arbitrary set. Their conditional distributions are shown to be a generalization of the hypergeometric distribution, while the marginal distributions can always be chosen as generalized binomial distributions. Then we propose sufficient conditions on the weight function ensuring that the marginal distributions are necessarily of the generalized binomial form. In these cases, the corresponding indicator random variables are conditionally independent (as in the classical De Finetti theorem) though they are neither exchangeable nor identically distributed.
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Full text: PDF
Pages: 72-86
Published on: January 19, 2009
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Bibliography
- Chow, Yuan Shih; Teicher, Henry. Probability theory.Independence, interchangeability, martingales.Second edition.Springer Texts in Statistics. Springer-Verlag, New York, 1988. xviii+467 pp. ISBN: 0-387-96695-1 MR0953964 (89e:60001)
- Diaconis, Persi; Freedman, David. The Markov moment problem and de Finetti's theorem. I. Math. Z. 247 (2004), no. 1, 183--199. MR2054525 (2005m:60004)
- Diaconis, Persi; Freedman, David. The Markov moment problem and de Finetti's theorem. II. Math. Z. 247 (2004), no. 1, 201--212. MR2054526 (2005m:60005)
- Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403 (42 #5292)
- Fristedt, Bert; Gray, Lawrence. A modern approach to probability theory.Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1997. xx+756 pp. ISBN: 0-8176-3807-5 MR1422917 (98e:60002)
- Gnedin, A.; Pitman, J. Exchangeable Gibbs partitions and Stirling triangles. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 325 (2005), Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 12, 83--102, 244--245; translation in J. Math. Sci. (N. Y.) 138 (2006), no. 3, 5674--5685 MR2160320 (2006h:60022)
- Hewitt, E., Savage, L.J. (1955). Symmetric measures on cartesian products. Trans. Amer. Math. Soc., 80, No. 2, pp. 470--501. MR0076206
- Kallenberg, Olav. Foundations of modern probability.Probability and its Applications (New York). Springer-Verlag, New York, 1997. xii+523 pp. ISBN: 0-387-94957-7 MR1464694 (99e:60001)
- Kerov, S.V. (2003). Asymptotic representation theory of the symmetric group and its applications in analysis. Translations of Mathematical Monographs 219. American Mathematical Society, Providence. MR1984868
- Ressel, Paul. De Finetti-type theorems: an analytical approach. Ann. Probab. 13 (1985), no. 3, 898--922. MR0799427 (86k:60023)
- Vélez Ibarrola, Ricardo; Prieto-Rumeau, Tomás. A De Finetti-type theorem for nonexchangeable finite-valued random variables. J. Math. Anal. Appl. 347 (2008), no. 2, 407--415. MR2440337
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Electronic Journal of Probability. ISSN: 1083-6489 |
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