Bernoulli

  • Bernoulli
  • Volume 21, Number 2 (2015), 1002-1013.

Stein factors for negative binomial approximation in Wasserstein distance

A.D. Barbour, H.L. Gan, and A. Xia

Full-text: Open access

Abstract

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 (2006) 943–954). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.

Article information

Source
Bernoulli, Volume 21, Number 2 (2015), 1002-1013.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1429624968

Digital Object Identifier
doi:10.3150/14-BEJ595

Mathematical Reviews number (MathSciNet)
MR3338654

Zentralblatt MATH identifier
1329.62077

Keywords
negative binomial approximation Stein factors Stein’s method Wasserstein distance

Citation

Barbour, A.D.; Gan, H.L.; Xia, A. Stein factors for negative binomial approximation in Wasserstein distance. Bernoulli 21 (2015), no. 2, 1002--1013. doi:10.3150/14-BEJ595. https://projecteuclid.org/euclid.bj/1429624968


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References

  • [1] Barbour, A.D. and Jensen, J.L. (1989). Local and tail approximations near the Poisson limit. Scand. J. Statist. 16 75–87.
  • [2] Barbour, A.D. and Xia, A. (2006). On Stein’s factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954.
  • [3] Brown, T.C. and Xia, A. (2001). Stein’s method and birth–death processes. Ann. Probab. 29 1373–1403.
  • [4] Kendall, D.G. (1948). On some modes of population growth leading to R. A. Fisher’s logarithmic series distribution. Biometrika 35 6–15.
  • [5] Kendall, D.G. (1952). Les processus stochastiques de croissance en biologie. Ann. Inst. H. Poincaré 13 43–108.
  • [6] Kretzschmar, M. (1989). A renewal equation with a birth–death process as a model for parasitic infections. J. Math. Biol. 27 191–221.
  • [7] Phillips, M.J. (1996). Stochastic process approximation and network applications. Ph.D. thesis, Univ. Melbourne.