Electronic Journal of Probability

De Finetti's-type results for some families of non identically distributed random variables

Ricardo Vélez Ibarrola and Tomas Prieto-Rumeau

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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.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 4, 72-86.

Dates
Accepted: 19 January 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819465

Digital Object Identifier
doi:10.1214/EJP.v14-602

Mathematical Reviews number (MathSciNet)
MR2471660

Zentralblatt MATH identifier
1190.60027

Subjects
Primary: 60G09: Exchangeability

Keywords
De Finetti theorem exchangeability random assignment processes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Vélez Ibarrola, Ricardo; Prieto-Rumeau, Tomas. De Finetti's-type results for some families of non identically distributed random variables. Electron. J. Probab. 14 (2009), paper no. 4, 72--86. doi:10.1214/EJP.v14-602. https://projecteuclid.org/euclid.ejp/1464819465


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