Neighbourhoods of independence for random processes

Details Neighbourhoods of independence for random processes Neighbourhoods of independence for random processes

2003-11-06

arxiv.org/abs/math/0311087v1

Mathematics

Differential Geometry

12 pages, 1 figure

Scientific paper

The Freund family of distributions becomes a Riemannian 4-manifold with Fisher information as metric; we derive the induced $\alpha$-geometry, i.e., the $\alpha$-curvature, $\alpha$-Ricci curvature with its eigenvales and eigenvectors, the $\alpha$-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.

Affiliated with

Also associated with

No associations

Rating

Neighbourhoods of independence for random processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Neighbourhoods of independence for random processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Neighbourhoods of independence for random processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-519484