On the nature of the binomial distribution
type: Item
instance of: scholarly article
title: On the nature of the binomial distribution
zbMATH Open document ID: 0987.60023
author: Abraham P. Punnen
author: P. Vellaisamy
published in: Journal of Applied Probability
publication date: 2002-06-23T00:00:00Z
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 1625605
zbMATH Keywords: sums of Bernoulli variables
zbMATH Keywords: binomial distribution
zbMATH Keywords: Poisson process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1239/jap/996986641
OpenAlex ID: W2089491659
DOI: 10.1239/JAP/996986641
review text: A sequence of Bernoulli variables \(\{X_i\}\) is considered. The sum of \(n\) those independent variables (a) has the binomial distribution \(B(n,p)\) with parameters \(n\) and \(p\), if \(P(X_i=1)= p\) for every \(i\) (b). This paper demonstates that \(B(n,p)\) arises also when both conditions (a and b) are violated. Especially, the structure of distributions of \(B(2,p)\) and \(B(3,p)\) for \(B(n,p)\) (\(n\) arbitrary) are obtained. The Poisson distribution for a random sum is characterized. This brings out the relationship between the Poisson process and the binomial distributions.
description: scientific article; zbMATH DE number 1625605