Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables

N. S. Upadhye () and P. Vellaisamy
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N. S. Upadhye: Indian Institute of Technology Madras
P. Vellaisamy: Indian Institute of Technology Bombay

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 4, 951-968

Abstract: Abstract 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.

Keywords: Compound negative binomial distribution; Compound Poisson distribution; Total variation distance; Compound Poisson approximation; Kerstan’s method; Method of exponents; Primary 60E05; Secondary 60F05; 60E15; 91B30 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-013-9352-9

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