How much information does the sequence of integer moments carry about the correspond- ing unknown absolutely continuous distribution? We prove that a reliable evaluation of the corresponding Shannon entropy can be done by exploiting some known theoretical results on the entropy convergence, uniquely involving exact moments without solving the underlying moment problem. All the procedure essentially rests on the solution of lin- ear systems, with nearly singular matrices, and hence it requires both calculations in high precision and a pre-conditioning technique. Numerical examples are provided to support the theoretical results.

Moment information and entropy evaluation for probability densities

Milev, Mariyan Nedelchev;Novi Inverardi, Pier Luigi;Tagliani, Aldo
2012-01-01

Abstract

How much information does the sequence of integer moments carry about the correspond- ing unknown absolutely continuous distribution? We prove that a reliable evaluation of the corresponding Shannon entropy can be done by exploiting some known theoretical results on the entropy convergence, uniquely involving exact moments without solving the underlying moment problem. All the procedure essentially rests on the solution of lin- ear systems, with nearly singular matrices, and hence it requires both calculations in high precision and a pre-conditioning technique. Numerical examples are provided to support the theoretical results.
2012
218
Milev, Mariyan Nedelchev; Novi Inverardi, Pier Luigi; Tagliani, Aldo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/90922
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