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

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Arwini K., Dodson C.

Open Mathematics

2007

tom 5

nr 1

50-83

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.

Ograniczanie wyników

1 Open Mathematics

1 Arwini K.

1 Dodson C.

1 2007

Wyniki wyszukiwania

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