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Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables

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Title Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables
 
Creator UPADHYE, N
VELLAISAMY, P
 
Subject Compound negative binomial distribution
Compound Poisson distribution
Total variation distance
Compound Poisson approximation
Kerstan's method
Method of exponents
ASYMPTOTIC EXPANSIONS
SUMS
 
Description In this paper, the problem of compound Poisson approximation to the convolution of compound negative binomial distributions, under total variation distance, is considered. First, we obtain an error bound using the method of exponents and it is compared with existing ones. It is known that Kerstan's method is more powerful in compound approximation problems. We employ Kerstan's method to obtain better estimates, using higher-order approximations. These bounds are of higher-order accuracy and improve upon some of the known results in the literature. Finally, an interesting application to risk theory is discussed.
 
Publisher SPRINGER
 
Date 2014-12-28T14:40:51Z
2014-12-28T14:40:51Z
2014
 
Type Article
 
Identifier METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 16(4)951-968
1387-5841
1573-7713
http://dx.doi.org/10.1007/s11009-013-9352-9
http://dspace.library.iitb.ac.in/jspui/handle/100/16778
 
Language English