The generalized maximum entropy principle

1989 ◽  
Vol 19 (5) ◽  
pp. 1042-1052 ◽  
Author(s):  
H.K. Kesavan ◽  
J.N. Kapur
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Generalized Maximum Entropy ◽  
Entropy Principle

scholarly journals (Generalized) Maximum Cumulative Direct, Residual, and Paired Φ Entropy Approach

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 91
Author(s):  
Ingo Klein ◽  
Monika Doll
Keyword(s):  
Maximum Entropy ◽  
Survival Function ◽  
Maximum Entropy Principle ◽  
Logistic Distribution ◽  
Generalized Maximum Entropy ◽  
Generalized Logistic Distribution ◽  
Entropy Principle ◽  
Bipolar Distribution ◽  
The One ◽  
Maximum Entropy Distributions

A distribution that maximizes an entropy can be found by applying two different principles. On the one hand, Jaynes (1957a,b) formulated the maximum entropy principle (MaxEnt) as the search for a distribution maximizing a given entropy under some given constraints. On the other hand, Kapur (1994) and Kesavan and Kapur (1989) introduced the generalized maximum entropy principle (GMaxEnt) as the derivation of an entropy for which a given distribution has the maximum entropy property under some given constraints. In this paper, both principles were considered for cumulative entropies. Such entropies depend either on the distribution function (direct), on the survival function (residual) or on both (paired). We incorporate cumulative direct, residual, and paired entropies in one approach called cumulative Φ entropies. Maximizing this entropy without any constraints produces an extremely U-shaped (=bipolar) distribution. Maximizing the cumulative entropy under the constraints of fixed mean and variance tries to transform a distribution in the direction of a bipolar distribution, as far as it is allowed by the constraints. A bipolar distribution represents so-called contradictory information, which is in contrast to minimum or no information. In the literature, to date, only a few maximum entropy distributions for cumulative entropies have been derived. In this paper, we extended the results to well known flexible distributions (like the generalized logistic distribution) and derived some special distributions (like the skewed logistic, the skewed Tukey λ and the extended Burr XII distribution). The generalized maximum entropy principle was applied to the generalized Tukey λ distribution and the Fechner family of skewed distributions. Finally, cumulative entropies were estimated such that the data was drawn from a maximum entropy distribution. This estimator will be applied to the daily S&P500 returns and time durations between mine explosions.

Generalized Maximum Entropy Principle, Superstatistics and Problem of Networks Classification

2011 ◽  
Author(s):  
Bahruz Gadjiev ◽  
Ali Mohammad-Djafari ◽  
Jean-François Bercher ◽  
Pierre Bessiére
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Generalized Maximum Entropy ◽  
Entropy Principle

scholarly journals Technical Note—A Generalized Maximum Entropy Principle

1979 ◽  
Vol 27 (6) ◽  
pp. 1188-1196 ◽  
Author(s):  
Marlin U. Thomas
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Technical Note ◽  
Generalized Maximum Entropy ◽  
Entropy Principle

An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

1990 ◽  
Vol 27 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Claudine Robert
Keyword(s):  
Artificial Intelligence ◽  
Maximum Entropy ◽  
Large Deviation ◽  
Maximum Entropy Principle ◽  
Statistical Modelling ◽  
Linear Constraints ◽  
Descriptive Statistics ◽  
Entropy Principle ◽  
Maximum Entropy Distribution ◽  
Mathematical Justification

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

Random quantal fields and maximum entropy principle

2005 ◽  
Author(s):  
Maciej M. Duras
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Entropy Principle

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

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