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Maximum Entropy Distribution with Constrained Mean

Pierre Dangauthier 1
1 E-MOTION - Geometry and Probability for Motion and Action
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, Inria Grenoble - Rhône-Alpes
Abstract : This note presents the derivation of the maximum entropy distribution of a real variable on the unit segment, when its first moment is constrained. The functional form of the resulting distribution is an exponential with two Lagrange multipliers. We show that there is unique solution for those multipliers. However this solution has to be numerically approximated. As a special case, we find the uniform distribution when the constrained mean is centered.
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Submitted on : Wednesday, September 5, 2007 - 2:35:27 PM
Last modification on : Wednesday, February 2, 2022 - 3:58:32 PM
Long-term archiving on: : Friday, November 25, 2016 - 4:51:19 PM


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  • HAL Id : inria-00167289, version 2



Pierre Dangauthier. Maximum Entropy Distribution with Constrained Mean. 2007. ⟨inria-00167289v2⟩



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