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Signed Poisson approximations for Markov chains

Author

Listed:
  • Cekanavicius, V.
  • Mikalauskas, M.

Abstract

Consider a sum of Markov dependent lattice variables. The normal approximation is trivial for this sum if the total variation distance is considered. Replacement of the normal approximation by its Poisson structured analogue changes the situation radically. Moreover, considering the Markov binomial distribution we prove that signed Poisson approximation can be more accurate than both the normal and Poisson approximations. Possible improvements due to asymptotic expansions are discussed.

Suggested Citation

  • Cekanavicius, V. & Mikalauskas, M., 1999. "Signed Poisson approximations for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 205-227, August.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:205-227
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    References listed on IDEAS

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    1. Hipp, Christian, 1986. "Improved Approximations for the Aggregate Claims Distribution in the Individual Model," ASTIN Bulletin, Cambridge University Press, vol. 16(2), pages 89-100, November.
    2. Borovkov, K. A. & Pfeifer, D., 1996. "Pseudo-Poisson approximation for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 163-180, January.
    3. Kuon, S. & Reich, A. & Reimers, L., 1987. "Panjer vs Kornya vs De Pril: A Comparison from a Practical Point of View," ASTIN Bulletin, Cambridge University Press, vol. 17(2), pages 183-191, November.
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    Cited by:

    1. Cekanavicius, V., 2002. "On the convergence of Markov binomial to Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 83-91, May.
    2. Cekanavicius, Vydas & Roos, Bero, 2009. "Poisson type approximations for the Markov binomial distribution," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 190-207, January.
    3. A. D. Barbour & Torgny Lindvall, 2006. "Translated Poisson Approximation for Markov Chains," Journal of Theoretical Probability, Springer, vol. 19(3), pages 609-630, December.

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