Gaussian distribution maximizes entropy for given covariance
Theorem 1
Let f:Rn→R be a continuous probability
density function. Let X1,…,Xn be random variables
with density f
and with covariance matrix K, Kij=cov(Xi,Xj). Let ϕ be the distribution
of the
multidimensional Gaussian (http://planetmath.org/JointNormalDistribution) with mean 0 and covariance matrix K. Then the Gaussian distribution maximizes the differential entropy for a given covariance matrix K. That is, h(ϕ)≥h(f).
Title | Gaussian distribution maximizes entropy for given covariance |
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Canonical name | GaussianDistributionMaximizesEntropyForGivenCovariance |
Date of creation | 2013-03-22 12:19:26 |
Last modified on | 2013-03-22 12:19:26 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 10 |
Author | Mathprof (13753) |
Entry type | Theorem |
Classification | msc 94A17 |