Polynomials Orthogonal with Respect to the Multinomial Distribution and the Factorial-Power Formalism

In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be computed the rate is determined by the lower bounds proved in this paper. General techniques for getting lower bounds in terms of moments are developed. The results about lower bound in the Law of Thin Numbers are used to derive similar results for the Central Limit Theorem.

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“…The original formula in[19] contains a typo in that the factor (−1) k+l is missing but the proof is correct.…”

mentioning

confidence: 99%

Thinning and information projections

Harremoës

Johnson

Kontoyiannis

2008

2008 IEEE International Symposium on Information Theory

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“…Tratnik introduced families of continuous and discrete multivariate orthogonal polynomials by means of the generalized Kampé de Fériet hypergeometric series [25,26], in particular multivariate Kravchuk polynomials. By using a combinatorial formalism, Khokhlov [27] introduced a family of polynomials orthogonal with respect to the multinomial distribution. Orthogonality relations of multivariate Kravchuk polynomials have been discussed by Mizukawa in [28].…”

Section: Bivariate Kravchuk Polynomialsmentioning

confidence: 99%

On limit relations between some families of bivariate hypergeometric orthogonal polynomials

Area¹,

Godoy²

2012

J. Phys. A: Math. Theor.

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In this paper we deal with limit relations between bivariate hypergeometric polynomials. We analyze the limit relation from trinomial distribution to bivariate Gaussian distribution, obtaining the limit transition from the second-order partial difference equation satisfied by bivariate hypergeometric Kravchuk polynomials to the second-order partial differential equation verified by bivariate hypergeometric Hermite polynomials. As a consequence the limit relation between both families of orthogonal polynomials is established. A similar analysis between bivariate Hahn and bivariate Appell orthogonal polynomials is also presented.

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