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On the nature of the binomial distribution

DSpace at IIT Bombay

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Field Value
 
Title On the nature of the binomial distribution
 
Creator VELLAISAMY, P
PUNNEN, AP
 
Subject successes
number
trials
sums of bernoulli variables
binomial distribution
statistical independence
characterizations
random sum
poisson distribution
poisson process
 
Description We examine how the binomial distribution B(n, p) arises as the distribution S-n = Sigma (n)(i=1) X-i of an arbitrary sequence of Bernoulli variables. It is shown that B(n, p) arises in infinitely many ways as the distribution of dependent and non-identical Bernoulli variables, and arises uniquely as that of independent Bernoulli variables. A number of illustrative examples are given. The cases B(2, p) and B(3, p) are completely analyzed to bring out some of the intrinsic properties of the binomial distribution. The conditions under which S-n follows B (n, p), given that Sn-1 is not necessarily a binomial variable, are investigated. Several natural characterizations of B(n, p), including one which relates the binomial distributions and the Poisson process, are also given. These results and characterizations lead to a better understanding of the nature of the binomial distribution and enhance the utility.
 
Publisher APPLIED PROBABILITY TRUST
 
Date 2011-07-18T09:55:39Z
2011-12-26T12:50:32Z
2011-12-27T05:35:49Z
2011-07-18T09:55:39Z
2011-12-26T12:50:32Z
2011-12-27T05:35:49Z
2001
 
Type Article
 
Identifier JOURNAL OF APPLIED PROBABILITY, 38(1), 36-44
0021-9002
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4867
http://hdl.handle.net/10054/4867
 
Language en