# 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…

### Table of Integrals, Series, and Products

- Mathematics
- 1943

Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special…