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

• Autorzy: Khadiga Arwini , Christopher Dodson
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Information geometry; statistical manifold; bivariate distribution; neighbourhoods of independence; exponential distribution; Freund distribution; Gaussian distribution

Kategorie tematyczne

• 60G05: Foundations of stochastic processes
• 53B20: Local Riemannian geometry

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 1
• Strony: 50-83

Daty

wydano

2007-03-01

online

2007-03-01

Twórcy

autor

Khadiga Arwini

• University of Manchester

autor

Christopher Dodson

• University of Manchester

Bibliografia

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• [2] S-I. Amari and H. Nagaoka: Methods of Information Geometry, American Mathematical Society, Oxford University Press, 2000.
• [3] Khadiga Arwini: Differential geometry in neighbourhoods of randomness and independence, PhD thesis, UMIST, 2004.
• [4] Khadiga Arwini and C.T.J. Dodson: “Information geometric neighbourhoods of randomness and geometry of the McKay bivariate gamma 3-manifold”, Sankhya: Indian Journal of Statistics, Vol. 66(2), (2004), pp. 211–231.
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Identyfikatory

DOI

10.2478/s11533-006-0034-5