Neighbourhoods of independence for random processes
| dc.creator | Arwini, Khadiga | |
| dc.creator | Dodson, C. T. J. | |
| dc.date | 2003-11-06 | |
| dc.date.accessioned | 2026-07-07T05:02:41Z | |
| dc.date.available | 2026-07-07T05:02:41Z | |
| dc.description | The Freund family of distributions becomes a Riemannian 4-manifold with Fisher information as metric; we derive the induced $α$-geometry, i.e., the $α$-curvature, $α$-Ricci curvature with its eigenvales and eigenvectors, the $α$-scalar curvature etc. We show that the Freund manifold has a positive constant 0-scalar curvature, so geometrically it constitutes part of a sphere. We consider special cases as submanifolds and discuss their geometrical structures; one submanifold yields examples of neighbourhoods of the independent case for bivariate distributions having identical exponential marginals. Thus, since exponential distributions complement Poisson point processes, we obtain a means to discuss the neighbourhood of independence for random processes. | |
| dc.description | 12 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0311087 | |
| dc.identifier | http://arxiv.org/abs/math/0311087 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69101 | |
| dc.subject | Differential Geometry | |
| dc.subject | Probability | |
| dc.subject | 53B20; 60G05 | |
| dc.title | Neighbourhoods of independence for random processes | |
| dc.type | text |