Gaussian distribution maximizes entropy for given covariance


Theorem 1

Let f:RnR be a continuous probability density functionMathworldPlanetmath. Let X1,,Xn be random variablesMathworldPlanetmath with density f and with covariance matrix K, Kij=cov(Xi,Xj). Let ϕ be the distributionPlanetmathPlanetmath 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
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