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  1. Home > Articles & Issues >
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  3. On Bernoulli Sums an ...
Conference paper

On Bernoulli Sums and Bernstein Polynomials

Jacek Cichoń (1), Zbigniew Gołębiewski (1)
(1) Faculty of Fundamental Problems of Technology [Wroclaw]
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Imported on
January 31, 2017
Published on
December 31, 2011
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
Proceedings
DOI
10.46298/dmtcs.2993
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https://about.hal.science/hal-authorisation-v1
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On Bernoulli Sums and Bernstein Polynomials

Jacek Cichoń (1), Zbigniew Gołębiewski (1)
(1) Faculty of Fundamental Problems of Technology [Wroclaw]
Abstract
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.
Keywords
  • [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]
  • asymptotic analysis
  • Bernoulli sums
  • Bernstein polynomials
  • entropy
  • binomial distribution
  • multinomial distribution
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