# 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

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topKhadiga 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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