Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions

Khadiga Arwini; Christopher Dodson

Open Mathematics (2007)

  • Volume: 5, Issue: 1, page 50-83
  • ISSN: 2391-5455

Abstract

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We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the topological character of the results makes them stable under small perturbations, which is important for applications in models of stochastic processes.

How to cite

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Khadiga Arwini, and Christopher Dodson. "Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions." Open Mathematics 5.1 (2007): 50-83. <http://eudml.org/doc/269244>.

@article{KhadigaArwini2007,
abstract = {We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the topological character of the results makes them stable under small perturbations, which is important for applications in models of stochastic processes.},
author = {Khadiga Arwini, Christopher Dodson},
journal = {Open Mathematics},
keywords = {Information geometry; statistical manifold; bivariate distribution; neighbourhoods of independence; exponential distribution; Freund distribution; Gaussian distribution; information geometry},
language = {eng},
number = {1},
pages = {50-83},
title = {Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions},
url = {http://eudml.org/doc/269244},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Khadiga Arwini
AU - Christopher Dodson
TI - Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions
JO - Open Mathematics
PY - 2007
VL - 5
IS - 1
SP - 50
EP - 83
AB - We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the topological character of the results makes them stable under small perturbations, which is important for applications in models of stochastic processes.
LA - eng
KW - Information geometry; statistical manifold; bivariate distribution; neighbourhoods of independence; exponential distribution; Freund distribution; Gaussian distribution; information geometry
UR - http://eudml.org/doc/269244
ER -

References

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  3. [3] Khadiga Arwini: Differential geometry in neighbourhoods of randomness and independence, PhD thesis, UMIST, 2004. 
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