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On the negative binomial distribution and its generalizations

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Title On the negative binomial distribution and its generalizations
 
Creator VELLAISAMY, P
UPADHYE, NS
 
Subject successes
trials
number
sums of random variables
characterizations
binomial moments
geometric distribution
negative binomial distribution
bernoulli sequences
probabilistic models
generalized negative binomial distributions
 
Description It is shown that the negative binomial distribution NB(r,p) may arise out of an identical but dependent geometric sequence. Using a general characterization result for NB(r,p), based on a non-negative integer (Z(+))-valued sequence, we show that NB(2,p) may arise as the distribution of the sum of Z(+)-valued random variables which are neither geometric nor independent. We show also that NB(r,p) arises, as the distribution of the number of trials for the rth success, based on a sequence of dependent Bernoulli variables. The generalized negative binomial distributions arising out of certain dependent Bernoulli sequences are also investigated. In particular, certain erroneous results in the literature are corrected. (c) 2006
 
Publisher ELSEVIER SCIENCE BV
 
Date 2011-07-25T23:49:54Z
2011-12-26T12:50:58Z
2011-12-27T05:37:13Z
2011-07-25T23:49:54Z
2011-12-26T12:50:58Z
2011-12-27T05:37:13Z
2007
 
Type Article
 
Identifier STATISTICS & PROBABILITY LETTERS, 77(2), 173-180
0167-7152
http://dx.doi.org/10.1016/j.spl.2006.06.008
http://dspace.library.iitb.ac.in/xmlui/handle/10054/6821
http://hdl.handle.net/10054/6821
 
Language en