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2 results

  • Poisson perturbations

  • Andrew D. Barbour, Aihua Xia
  • Journal:
    ESAIM: Probability and Statistics / Volume 3 / 1999
    Published online by Cambridge University Press:
    15 August 2002, pp. 131-150
    Print publication:
    1999

  • Stein's method is used to prove approximations in total variation to thedistributions of integer valued random variables by (possibly signed)compound Poisson measures. For sums of independent random variables,the results obtained are very explicit, and improve upon earlierwork of Kruopis (1983) and Čekanavičius (1997);coupling methods are used to derive concrete expressions for the errorbounds. An example is given to illustrate the potential for applicationto sums of dependent random variables.