A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean

Gzyl, Henryk; Horst, Enrique ter

doi:10.3390/e16021123

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…The requirement for maximum generalized entropy with limited headroom requirement is equivalent to a minimum consumption of these resources for the system of restrictions granularity of the system must not be below a certain threshold [9,10].…”

Section: Resultmentioning

confidence: 99%

Paradigm Control of Complex Technical Systems

Bublichenko¹

2015

ujca

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The problems associated with the concept of extreme principle, structural decomposition, entropy and the possibility of using the methods of the theory of categories. The most common results of statements of problems and mathematical models of management in the structure of the cutting technology the semiconductor ingots and other functional materials for thin plates for the preparation of base layers for the micro-and nanoelectronic devices are presented.

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Section: Resultmentioning

confidence: 99%

Paradigm Control of Complex Technical Systems

Bublichenko¹

2015

ujca

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“…For applications to problems such as (1), (5), (7), see Gzyl and Mayoral [27,28]. To conclude the short digression about maximum entropy on the mean, we mention here that it is much more general and flexible than the standard method of maximum entropy, and contains a particular case (see Gzyl and ter Horst [29]). Such extension is a good tool for solving problems such as (3), (6), (8).…”

Section: Comments About the Solutions To The Generalized Moment And Imentioning

confidence: 99%

Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory

Gzyl

Mayoral

2017

Entropy

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Abstract:Here, we consider the following inverse problem: Determination of an increasing continuous function U(x) on an interval [a, b] from the knowledge of the integrals U(x)dF X i (x) = π i where the X i are random variables taking values on [a, b] and π i are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when U(x) is supposed to have a positive derivative, and it becomes a classical interpolation problem if the X i are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems.

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