Probability distributions arising from nested Gaussians

Souad El Outmani 1 Armand Maul 1, 2
2 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : We consider a random sample X1,...,Xn of size n⩾1 from an View the MathML source Gaussian law. Then, conditionally on each View the MathML source, we define a new random sample Xi,1,...,Xi,n from the View the MathML source normal distribution (View the MathML source is notation introduced for convenience). Assuming that the so obtained n new random samples are conditionally independent, we get a second step randomly generated set of points. The question is to investigate the properties of this set. We give a theorem precising the limiting density obtained when n approaches infinity, and we generalize this theorem by studying what occurs when repeating this process until, conditionally on each View the MathML source, we get new random samples View the MathML source, from the View the MathML source normal distribution
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Article dans une revue
Comptes Rendus Mathématique, Elsevier Masson, 2009, 347 (3-4), pp.201-204. 〈http://www.sciencedirect.com/science/article/pii/S1631073X09000235〉. 〈10.1016/j.crma.2009.01.009〉
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https://hal.inria.fr/hal-00772434
Contributeur : Ist Inria Nancy Grand Est <>
Soumis le : jeudi 10 janvier 2013 - 14:59:08
Dernière modification le : jeudi 11 janvier 2018 - 06:23:18

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Souad El Outmani, Armand Maul. Probability distributions arising from nested Gaussians. Comptes Rendus Mathématique, Elsevier Masson, 2009, 347 (3-4), pp.201-204. 〈http://www.sciencedirect.com/science/article/pii/S1631073X09000235〉. 〈10.1016/j.crma.2009.01.009〉. 〈hal-00772434〉

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