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Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables

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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.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    N. S. Upadhye

  2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    P. Vellaisamy

Authors
  1. N. S. Upadhye
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  2. P. Vellaisamy
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Correspondence to N. S. Upadhye.

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Upadhye, N.S., Vellaisamy, P. Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables. Methodol Comput Appl Probab 16, 951–968 (2014). https://doi.org/10.1007/s11009-013-9352-9

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  • DOI: https://doi.org/10.1007/s11009-013-9352-9

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