Jacek Cichoń ; Zbigniew Gołębiewski - On Bernoulli Sums and Bernstein Polynomials

dmtcs:2993 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) - https://doi.org/10.46298/dmtcs.2993
On Bernoulli Sums and Bernstein Polynomials

Authors: Jacek Cichoń 1; Zbigniew Gołębiewski 1

  • 1 Faculty of Fundamental Problems of Technology [Wroclaw]

In the paper we discuss a technology based on Bernstein polynomials of asymptotic analysis of a class of binomial sums that arise in information theory. Our method gives a quick derivation of required sums and can be generalized to multinomial distributions. As an example we derive a formula for the entropy of multinomial distributions. Our method simplifies previous work of Jacquet, Szpankowski and Flajolet from 1999.

https://doi.org/10.46298/dmtcs.2993
Source: HAL:hal-01197242v1
Volume: DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: asymptotic analysis,Bernoulli sums,Bernstein polynomials,entropy,binomial distribution,multinomial distribution,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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