Binomial mixtures and finite exchangeability
type: Item
instance of: scholarly article
title: Binomial mixtures and finite exchangeability
zbMATH Open document ID: 0759.60010
published in: The Annals of Probability
publication date: 1993-01-17T00:00:00Z
review text: Let \(\{h(i| p)\}^ n_{i=0}\) be the binomial distribution with parameter \(p\). If \(p\) moves from 0 to 1, the point \((h(0| p),\dots,h(n| p))\) traces a curve \(B_ n\) in the simplex \(T_ n=\{(x_ 0,\dots,x_ n)\): \(\sum^ n_{i=0}x_ i=1\) and \(x_ i\geq 0\) for all \(i\}\). Let \(\text{co} B_ n\) stand for the convex hull of \(B_ n\). The author shows that \[ v(\text{co} B_ n)/v(T_ n)=(n!)^ n\prod^ n_{k=1}1/(2k-1)!, \] where \(v(A)\) stands for the \(n\)- dimensional volume of \(A\). This result is connected with the problem of extending \(n\)-exchangeable sequences of \(\{0,1\}\)-valued random variables to infinite exchangeable sequences.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60G09
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 97388
zbMATH Keywords: binomial distribution
zbMATH Keywords: simplex
zbMATH Keywords: convex hull
zbMATH Keywords: exchangeable sequences
author: Graham R. Wood
reviewed by: Aurel Spătaru
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989684
OpenAlex ID: W2076411009
DOI: 10.1214/AOP/1176989684
description: scientific article; zbMATH DE number 97388