On the rate of Poisson approximation to Bernoulli partial sum processes

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Abstract

We investigate approximation of a Bernoulli partial sum process to the accompanying Poisson process in the non-i.i.d. case. The rate of closeness is studied in terms of the minimal distance in probability. In particular, a new lower bound for the total variation distance between a Bernoulli partial sum process and the accompanying Poisson process is obtained.

Original languageEnglish
Article number108754
Number of pages7
JournalStatistics and Probability Letters
Volume162
DOIs
Publication statusPublished - Jul 2020

Keywords

  • Bernoulli random variables
  • Minimal distance
  • Partial sum process
  • Poisson approximation
  • Total variation distance
  • DISTANCES
  • TERMS
  • PROBABILITY-MEASURES
  • UNBOUNDED FUNCTIONS
  • EXPECTATIONS
  • RANDOM-VARIABLES
  • ACCURACY

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