Open AccessGAUSS APPROXIMATION FOR NUMBER DISTRIBUTION IN OF A PASCAL’S TRIANGLE
Author(s) -
I. M. Abramov,
Grigory Abramov
Publication year - 2021
Publication title -
žurnal občislûvalʹnoï ta prikladnoï matematiki
Language(s) - English
Resource type - Journals
eISSN - 2706-9699
pISSN - 2706-9680
DOI - 10.17721/2706-9699.2021.1.01
Subject(s) - binomial coefficient , multinomial distribution , pascal (unit) , mathematics , trinomial , binomial theorem , gauss , distribution (mathematics) , notice , distribution function , combinatorics , mathematical analysis , calculus (dental) , statistics , physics , medicine , dentistry , political science , law , quantum mechanics
We received normal distribution parameters that approximates the distribution of numbers in the n-th row of Pascal's triangle. We calculated the values for normalized moments of even orders and shown their asymptotic tendency towards values corresponding to a normal distribution. We have received highly accurate approximations for central elements of even rows of Pascal's triangle, which allows for calculation of binomial, as well as trinomial (or, in general cases, multinomial) coefficients. A hypothesis is proposed, according to which it is possible that physical and physics-chemical processes function according to Pascal's distribution, but due to how slight its deviation is from a normal distribution, it is difficult to notice. It is also possible that as technology and experimental methodology improves, this difference will become noticeable where it is traditionally considered that a normal distribution is taking place.