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On the Rate of Multivariate Poisson Convergence

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  • Roos, Bero

Abstract

The distribution of the sum of independent nonidentically distributed Bernoulli random vectors inRkis approximated by a multivariate Poisson distribution. By using a multivariate adaption of Kerstan's (1964,Z. Wahrsch. verw. Gebiete2, 173-179) method, we prove a conjecture of Barbour (1988,J. Appl. Probab.25A, 175-184) on removing a log-term in the upper bound of the total variation distance. Second-order approximations are included.

Suggested Citation

  • Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    • Handle: RePEc:eee:jmvana:v:69:y:1999:i:1:p:120-134
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    References listed on IDEAS

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    1. Deheuvels, Paul & Pfeifer, Dietmar, 1988. "Poisson approximations of multinomial distributions and point processes," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 65-89, April.
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    Cited by:

    1. Marco Faravelli & Priscilla Man, 2021. "Generalized majority rules: utilitarian welfare in large but finite populations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 21-48, July.
    2. Novak, S.Y. & Xia, A., 2012. "On exceedances of high levels," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 582-599.
    3. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    4. Krishna, Vijay & Morgan, John, 2012. "Voluntary voting: Costs and benefits," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2083-2123.
    5. Upadhye, N.S. & Vellaisamy, P., 2013. "Improved bounds for approximations to compound distributions," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 467-473.
    6. Vijay Krishna & John Morgan, 2015. "Majority Rule and Utilitarian Welfare," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 339-375, November.
    7. Kruopis, Julius & Čekanavičius, Vydas, 2014. "Compound Poisson approximations for symmetric vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 30-42.
    8. 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.

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