MyJournals Home  

RSS FeedsEntropy, Vol. 22, Pages 91: (Generalized) Maximum Cumulative Direct, Residual, and Paired ? Entropy Approach (Entropy)

 
 

12 january 2020 04:02:54

 
Entropy, Vol. 22, Pages 91: (Generalized) Maximum Cumulative Direct, Residual, and Paired ? Entropy Approach (Entropy)
 




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.


Del.icio.us Digg Facebook Google StumbleUpon Twitter
 
53 viewsCategory: Informatics, Physics
 
Entropy, Vol. 22, Pages 90: How the Probabilistic Structure of Grammatical Context Shapes Speech (Entropy)
Entropy, Vol. 22, Pages 93: Introduction to Extreme Seeking Entropy (Entropy)
 
 
blog comments powered by Disqus


MyJournals.org
The latest issues of all your favorite science journals on one page

Username:
Password:

Register | Retrieve

Search:

Physics

Use these buttons to bookmark us:
Del.icio.us Digg Facebook Google StumbleUpon Twitter


Valid HTML 4.01 Transitional
Copyright © 2008 - 2020 Indigonet Services B.V.. Contact: Tim Hulsen. Read here our privacy notice.
Other websites of Indigonet Services B.V.: Nieuws Vacatures News Tweets Travel Photos Nachrichten Indigonet Finances Leer Mandarijn