Volume 9, Issue 4
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Neighbourhoods of Independence for Random Processes via Information Geometry
3. Concluding Remarks
We have derived the information geometry of the 4-manifold of Freund bivariate mixture exponential distributions, which admits positive and negative covariance. The -curvature objects are derived for and those on four submanifolds, including the case of statistically independent random variables and the special case ACBED of Block and Basu. We provide examples of neighbourhoods of the independent case for bivariate distributions having identical exponential marginals and zero covariance. The Freund manifold has a constant 0-scalar curvature, so geometrically it constitutes part of a sphere.
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