We describe new families of discrete distributions that are used to model sums of exchangeable Bernoulli random variables. These discrete distributions can be parameterized in terms of their range, ...
Exchangeability refers to the property of a sequence or collection of random variables whereby its joint probability distribution remains unchanged under any finite permutation of indices. This ...
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Canada. Department of Mathematical Sciences, University of New Brunswick, Saint John, Canada. The celebrated Gnedenko-Raikov ...
ABSTRACT: We study the connection between the central limit theorem and law of large numbers for exchangeable sequences, and provide a counterexample to the Gnedenko-Raikov theorem for such sequences.
Abstract: We review information-theoretic approaches to obtaining simple probabilistic representations for sequences of exchangeable random variables. Specifically, we examine information-theoretic ...
Abstract: Wyner defined the notion of common information of two discrete random variables as the minimum of I(W; X,Y) where W induces conditional independence between X and Y. Its generalization to ...
This repository hosts a Lean 4 companion project for Seongchan Lee and Ilmun Kim, A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables. The project explores how Lean can make ...
A finite set of random variables $\lbrace X_1,\ldots,X_n \rbrace$ defined on a common probablility space $(\Omega, \mathcal{F}, P)$ is said to be \emph{exchangeable ...
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