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
NULL##NULL
Jacek Cichoń;Zbigniew Gołębiewski
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.
Volume: DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)