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ON THE SUMS OF COMPOUND NEGATIVE BINOMIAL AND GAMMA RANDOM VARIABLES

DSpace at IIT Bombay

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Title ON THE SUMS OF COMPOUND NEGATIVE BINOMIAL AND GAMMA RANDOM VARIABLES
 
Creator VELLAISAMY, P
UPADHYE, NS
 
Subject compound negative binomial distribution
convolution
random parameter representation
compound poisson distribution
sums of gamma random variables
poisson process
 
Description We study the convolution of compound negative binomial distributions with arbitrary parameters. The exact expression and also a random parameter representation are obtained. These results generalize some recent results in the literature. An application of these results to insurance mathematics is discussed. The sums of certain dependent compound Poisson variables are also studied. Using the connection between negative binomial and gamma distributions, we obtain a simple random parameter representation for the convolution of independent and weighted gamma variables with arbitrary parameters. Applications to the reliability of m-out-of-n:G systems and to the shortest path problem in graph theory are also discussed.
 
Publisher APPLIED PROBABILITY TRUST
 
Date 2011-07-18T09:58:28Z
2011-12-26T12:50:32Z
2011-12-27T05:35:50Z
2011-07-18T09:58:28Z
2011-12-26T12:50:32Z
2011-12-27T05:35:50Z
2009
 
Type Article
 
Identifier JOURNAL OF APPLIED PROBABILITY, 46(1), 272-283
0021-9002
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4868
http://hdl.handle.net/10054/4868
 
Language en