Open Access
August 2013 Extendibility of Marshall–Olkin distributions and inverse Pascal triangles
Jan-Frederik Mai, Matthias Scherer
Braz. J. Probab. Stat. 27(3): 310-321 (August 2013). DOI: 10.1214/11-BJPS158


Necessary and sufficient conditions are derived on the parameters of a $d$-dimensional random vector with Marshall–Olkin distribution to be extendible to an infinite exchangeable sequence. Interpreted differently, this result allows to decide if the respective multivariate exponential distribution can be constructed by means of a model with conditionally independent and identically distributed components. The proof makes use of the solution of the truncated Hausdorff moment problem and a reparameterization of the Marshall–Olkin distribution.


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Jan-Frederik Mai. Matthias Scherer. "Extendibility of Marshall–Olkin distributions and inverse Pascal triangles." Braz. J. Probab. Stat. 27 (3) 310 - 321, August 2013.


Published: August 2013
First available in Project Euclid: 28 May 2013

zbMATH: 1298.62083
MathSciNet: MR3064726
Digital Object Identifier: 10.1214/11-BJPS158

Keywords: de Finetti’s theorem , Lévy subordinator , Marshall–Olkin distribution , Pascal’s triangle , truncated Hausdorff’s moment problem

Rights: Copyright © 2013 Brazilian Statistical Association

Vol.27 • No. 3 • August 2013
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