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Neighbourhoods of Randomness and the Information Geometry of the Mckay Bivariate Gamma 3-manifold
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| Department: | Department of Mathematics |
| Organization: | Department of Mathematics, University of Toronto |
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2003 International Mathematica Symposium
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Imperial College, London
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We showed [3] that gamma distributions provide models for departures from randomness, since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. Here we use Mathematica to illustrate these neighbourhoods. Using Mathematica, without which the computations would have been prohibitively tedious, we derived also the information geometry of the 3-manifold of Mckay bivariate gamma distributions, which can provide a metrization of departures from randomness and independence for bivariate processes. As in the case of bivariate normal manifolds, we have negative scalar curvature, but here it is not constant; details are provided in our paper [3].
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information geometry, Mckay Bivariate Gamma 3-manifold, gamma distributions, exponential distribution, information theoretic metric topology, scalar curvature, randomness
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