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Journal Articles Comptes Rendus. Mathématique Year : 2009

Probability distributions arising from nested Gaussians

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

Dates and versions

hal-00772434 , version 1 (10-01-2013)

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Cite

Souad El Outmani, Armand Maul. Probability distributions arising from nested Gaussians. Comptes Rendus. Mathématique, 2009, 347 (3-4), pp.201-204. ⟨10.1016/j.crma.2009.01.009⟩. ⟨hal-00772434⟩
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