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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/6821

Title: On the negative binomial distribution and its generalizations
Authors: VELLAISAMY, P
UPADHYE, NS
Keywords: successes
trials
number
Issue Date: 2007
Publisher: ELSEVIER SCIENCE BV
Citation: STATISTICS & PROBABILITY LETTERS, 77(2), 173-180
Abstract: 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
URI: 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
ISSN: 0167-7152
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