Entropies of deformed binomial distributions
@article{Bergeron2014EntropiesOD, title={Entropies of deformed binomial distributions}, author={Herv{\'e} Bergeron and Evaldo M. F. Curado and J. P. Gazeau and Ligia M.C.S. Rodrigues}, journal={arXiv: Statistical Mechanics}, year={2014} }
Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies are studied through three examples. The first one derives from theq-exponential as a generating function. The second one involves the modified Abel polynomials, and the third one involves Hermite polynomials. The former and the latter have extensive Boltzmann-Gibbs whereas the ⇣
References
SHOWING 1-10 OF 23 REFERENCES
Possible generalization of Boltzmann-Gibbs statistics
- Physics
- 1988
With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelySq ≡k [1 – ∑i=1W piq]/(q-1), whereq∈ℝ characterizes the generalization andpi are the…
Generating functions for generalized binomial distributions
- Mathematics
- 2012
In a recent article generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal probability…
Symmetric generalized binomial distributions
- Mathematics
- 2013
In two recent articles, we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the…
On a Generalization of the Binomial Distribution and Its Poisson-like Limit
- Mathematics
- 2012
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum…
Nonextensive foundation of Lévy distributions.
- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999
It is argued on physical grounds that normalized q-expectation values should be used instead and the Lévy problem is revisit and it is verified that the relevant analytic results become sensibly simplified, whereas the basic physics remains unchanged.
Generalized binomial distributions
- Mathematics
- 1993
In many cases where the binomial dismbution fails to apply to real world data it is because of more variability in the data than can be explained by that dismbution. Several authors have proposed…
Nonadditive entropy and nonextensive statistical mechanics - An overview after 20 years
- Physics
- 2009
Statistical mechanics constitutes one of the pillars of contemporary physics. Recognized as such — together with mechanics (classical, quantum, relativistic), electromagnetism and thermodynamics —,…
Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example
- Mathematics
- 2009
AbstractExtremization of the Boltzmann-Gibbs (BG) entropy
$S_{BG}=-k\int dx\,p(x) \ln p(x)$ under appropriate norm and width constraints yields the Gaussian distribution
pG(x) ∝e-βx. Also, the basic…
On Measures of Entropy and Information
- Computer Science
- 2015
This book is an updated version of the information theory classic, first published in 1990, and includes expanded treatment of stationary or sliding-block codes and their relations to traditional block codes and discussion of results from ergodic theory relevant to information theory.