2005.42: Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions
2005.42: Khadiga Arwini and CTJ Dodson (2007) Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions. Central European Journal of Mathematics, 51. pp. 50-83. ISSN 1644-3616
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Abstract
We provide explicit information geometric tubular neighbourhoods containing all bivariate processes 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 alpha-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate processes; the topological character of the results makes them stable under small perturbations, which is important for applications.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | information geometry, statistical manifold, neighbourhoods of independence, exponential distribution, Freund distribution, Gaussian distribution |
| Subjects: | MSC 2000 > 53 Differential geometry MSC 2000 > 60 Probability theory and stochastic processes |
| MIMS number: | 2005.42 |
| Deposited By: | Prof CTJ Dodson |
| Deposited On: | 04 June 2007 |
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