Skip to Main content Skip to Navigation
Journal articles

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
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/hal-00772434
Contributor : Ist Inria Nancy Grand Est <>
Submitted on : Thursday, January 10, 2013 - 2:59:08 PM
Last modification on : Monday, July 19, 2021 - 4:40:03 PM

Identifiers

Collections

Citation

Souad El Outmani, Armand Maul. Probability distributions arising from nested Gaussians. Comptes Rendus. Mathématique, Centre Mersenne (2020-..) ; Elsevier Masson (2002-2019), 2009, 347 (3-4), pp.201-204. ⟨10.1016/j.crma.2009.01.009⟩. ⟨hal-00772434⟩

Share

Metrics

Record views

424