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Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables

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  • N. S. Upadhye

    (Indian Institute of Technology Madras)

  • P. Vellaisamy

    (Indian Institute of Technology Bombay)

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.

Suggested Citation

  • N. S. Upadhye & P. Vellaisamy, 2014. "Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 951-968, December.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:4:d:10.1007_s11009-013-9352-9
    DOI: 10.1007/s11009-013-9352-9
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    References listed on IDEAS

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    1. Vellaisamy, P. & Chaudhuri, B., 1999. "On compound Poisson approximation for sums of random variables," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 179-189, January.
    2. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    3. Gerber, Hans U., 1984. "Error bounds for the compound poisson approximation," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 191-194, July.
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    Cited by:

    1. L. Beghin & P. Vellaisamy, 2018. "Space-Fractional Versions of the Negative Binomial and Polya-Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 463-485, June.

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