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An efficient algorithm to generate maximum entropy distributions
Author(s) -
Basu P. C.,
Templeman A. B.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200607
Subject(s) - principle of maximum entropy , maximum entropy spectral estimation , maximum entropy probability distribution , notation , mathematics , algorithm , probabilistic logic , entropy (arrow of time) , scaling , mathematical optimization , statistics , geometry , physics , arithmetic , quantum mechanics
The paper describes an algorithm for generating maximum entropy distributions for probabilistic data. The central moments of the data form constraint equations developed from Jaynes' formalism, which are solved by mathematical programming. Criteria are presented for selecting starting points and scaling parameters, upon which the accuracy and efficiency of the algorithm depends. Results are given of tests in which maximum entropy distributions are generated from the moment information of numerous analytical distributions. They show that four moments are generally required to produce good agreement and that maximum entropy distributions can represent most data populations very well. The notation used in the paper is defined in Appendix I.